Vereenvoudig indien mogelijk.
\( \frac {(b - a)^3} {a^2 - b^2 } =\answer [onlineshowanswerbutton]{\frac {-(a - b)^2} {a + b} } \)
\( \frac {x^2 + 1} {x^4 + 2x^2 + 1 } =\answer [onlineshowanswerbutton]{\frac {1} {x^2 + 1} } \)
\( \frac {4x^2 - 12xy + 9y^2} {4x^2 - 9y^2 } =\answer [onlineshowanswerbutton]{\frac {2x - 3y} {2x + 3y} } \)
\( \frac {(2x - y)^2 - (x + 3y)^2} {(3x - y)^2 - (2x + 3y)^2 } =\answer [onlineshowanswerbutton]{\frac {3x + 2y} {5x + 2y} } \)
\( \frac {a^2 b + ac - ab^2 c - bc^2} {a^2 c - ab - abc^2 + b^2 c} =\answer [onlineshowanswerbutton]{\frac {ab + c} {ac - b} } \)
\( \frac {x^3 - 8} {2x^3 + 2x^2 - 8x - 8 } =\answer [onlineshowanswerbutton]{\frac {x^2 + 2x + 4} {2(x + 2)(x + 1)} } \)
\( \frac {(x - 3)(x - 2) - 2} {x - 1 } =\answer [onlineshowanswerbutton]{x - 4 } \)
\( \frac {(x - 2)(x + 5) + (x + 1)} {x - 2 } =\answer [onlineshowanswerbutton]{\frac {x^2 + 4x - 9} {x - 2} } \)
\( \frac {2a(a + 2) - (a^2 - a - 6)} {(a + 2)^3 } =\answer [onlineshowanswerbutton]{\frac {a + 3} {(a + 2)^2} } \)
\( \frac {x^3 + 3x^2 + 3x + 1} {-2x^3 - 8x^2 - 10x - 4 } =\answer [onlineshowanswerbutton]{\frac {-(x + 1)} {2(x + 2)} } \)
Vereenvoudig indien mogelijk. Zonder eerst in teller en noemer de gemeenschappelijke
factoren af.
\( \frac {3x^4 - 3x^2} {x^4 + x^2 } =\answer [onlineshowanswerbutton]{\frac {3(x^2 - 1)}{x^2 + 1} } \)
\( \frac {a^2 - ab} {b^2 - ab } =\answer [onlineshowanswerbutton]{-\frac {a}{b} } \)
\( \frac {a^2 - a^6} {-a^7 + a^5 } =\answer [onlineshowanswerbutton]{\frac {a^2 + 1}{a^3} } \)
\( \frac {2(x - 2) + (x - 2)x^2} {x - 2 } =\answer [onlineshowanswerbutton]{x^2 + 2 } \)
\( \frac {(4a - 1)b + (1 - 4a)c} {b - c } =\answer [onlineshowanswerbutton]{4a - 1 } \)
\( \frac {x^3 + 6x^2 + 9x} {x^3 - 9x } =\answer [onlineshowanswerbutton]{\frac {x + 3}{x - 3} } \)
\( \frac {2x - 1 + (2x - 1)^2} {(2x - 1)^3 } =\answer [onlineshowanswerbutton]{\frac {2x}{(2x - 1)^2} } \)
\( -\frac { (x - 1)^3 - 3(x + 1)(1 - x)^2}{(x - 1)^6 } =\answer [onlineshowanswerbutton]{\frac {2(x + 2)}{(x - 1)^4} } \)
\( \frac {2a(a^2 + 3) - a^2 \cdot 2a} {a(a^2 + 3)^2 } =\answer [onlineshowanswerbutton]{\frac {6}{(a^2 + 3)^2} } \)
\( \frac {ax + bx + ay + by + az + bz} {a + b } =\answer [onlineshowanswerbutton]{x + y + z } \)
Bereken en vereenvoudig indien mogelijk.
\( \frac {3} {x + 1} + \frac {2x + 1} {x - 2} =\answer [onlineshowanswerbutton]{\frac {2x^2 + 6x - 5}{(x - 2)(x + 1)} } \)
\( \frac {2x + 3} {2x - 3} + \frac {7} {x} =\answer [onlineshowanswerbutton]{\frac {17a + 3}{3(a + 2)} } \)
\( \frac {4a + 1} {a + 2} + \frac {5a} {3(a + 2)} =\answer [onlineshowanswerbutton]{\frac {2x^2 + 17x - 21}{x(2x - 3)} } \)
\( \frac {4x + 1} {2x - 3} + \frac {2x + 4} {3 - 2x} =\answer [onlineshowanswerbutton]{1 } \)
\( 1 - \frac {x - 2} {3x + 7} =\answer [onlineshowanswerbutton]{\frac {2x + 9}{3x + 7} } \)
\( \frac {a} {5} - \frac {a + 2} {3a} =\answer [onlineshowanswerbutton]{\frac {3a^2 - 5a - 10}{15a} } \)
\( \frac {2x - 1} {x - 5} + \frac {x + 5} {2x + 1} =\answer [onlineshowanswerbutton]{\frac {5x^2 - 26}{(x - 5)(2x + 1)} } \)
\( \frac {x - 4} {x - 1} - \frac {x - 1} {x - 4} =\answer [onlineshowanswerbutton]{\frac {-3(2x - 5)}{(x - 4)(x - 1)} } \)
\( \frac {x} {x - 4} + \frac {x - 8} {x - 4} =\answer [onlineshowanswerbutton]{2 } \)
\( \frac {a} {a - 2} + \frac {2a - 1} {2 - a} =\answer [onlineshowanswerbutton]{\frac {-(a - 1)}{a - 2} } \)
Bereken en vereenvoudig indien mogelijk.
\( \frac {2a^2} {(a - 1)(a + 1)} - \frac {a^2 + 1} {a^2 - 1} =\answer [onlineshowanswerbutton]{1 } \)
\( \frac {1} {(a - b)^2} + \frac {1} {(b - a)^2} =\answer [onlineshowanswerbutton]{\frac {2}{(a - b)^2} } \)
\( \frac {1} {x - 1} + \frac {x + 1} {(x - 1)(x - 3)} =\answer [onlineshowanswerbutton]{\frac {2}{x - 3} } \)
\( \frac {8} {(2 + x)(x - 2)} + \frac {2} {2 - x} =\answer [onlineshowanswerbutton]{\frac {-2}{x + 2} } \)
\( \frac {1} {x + 1} + \frac {1} {x - 1} + \frac {2}{(1 - x)(1 + x)} =\answer [onlineshowanswerbutton]{\frac {2}{x + 1} } \)
\( \frac {4} {2 + x} - \frac {8} {4 - x^2} + \frac {2}{x - 2} =\answer [onlineshowanswerbutton]{\frac {2(3x + 2)}{(x - 2)(x + 2)} } \)
\( \frac {x - 1} {2x - 1} + \frac {2} {x - 1} - \frac {x}{1 - 2x} =\answer [onlineshowanswerbutton]{\frac {x + 1}{x - 1} } \)
\( \frac {5x - 9} {(x + 2)(x - 3)} + \frac {x - 3} {(x + 1)(x + 2)} =\answer [onlineshowanswerbutton]{\frac {2x(3x - 5)}{(x + 1)(x + 2)(x - 3)} } \)
\( \frac {x - 3} {(x - 1)(x - 2)} - \frac {x - 1} {(x - 2)(x - 3)} =\answer [onlineshowanswerbutton]{\frac {-4}{(x - 3)(x - 1)} } \)
\( \frac {2x - 3} {(2x - 1)(x - 1)} + \frac {x + 3} {(2x - 1)(2x + 3)} =\answer [onlineshowanswerbutton]{\frac {5x^2 + 2x - 12}{(x - 1)(2x - 1)(2x + 3)} } \)
Bereken en vereenvoudig indien mogelijk.
\( \frac {x + 6} {x^2 - 16} - \frac {x + 1} {x^2 - 4x } =\answer [onlineshowanswerbutton]{\frac {1}{x(x + 4)} } \)
\( \frac {x + 1} {x - 1} + \frac {x - 1} {x + 1} - \frac {4}{x^2 - 1 } =\answer [onlineshowanswerbutton]{2 } \)
\( \frac {4x} {x^2 - 4} + \frac {2} {x^2 - 5x + 6 } =\answer [onlineshowanswerbutton]{\frac {2(2x - 1)}{(x - 3)(x + 2)} } \)
\( \frac {3} {x^3 - 1} - \frac {2} {x^2 - 1 } =\answer [onlineshowanswerbutton]{\frac {-(2x + 1)}{(x + 1)(x^2 + x + 1)} } \)
\( \frac {1} {x^2 - x - 2} - \frac {1} {x^3 - 4x^2 + 5x - 2 } =\answer [onlineshowanswerbutton]{\frac {x(x - 3)}{(x - 2)(x + 1)(x^2 - 2x + 1)} } \)
\( \frac {a^3 - b^3} {a^2 - b^2} - \frac {a^2 b + ab^2} {a^2 + ab } =\answer [onlineshowanswerbutton]{\frac {a^2}{a + b} } \)
\( \frac {a^4} {a^4- b^4} + \frac {1} {a^2 - b^2 -1 } =\answer [onlineshowanswerbutton]{\frac {a^2 + b^2 + b^4}{a^4 - b^4} } \)
\( \frac {1} {x - y} - \frac {3xy} {x^3 - y^3 } =\answer [onlineshowanswerbutton]{\frac {x - y}{x^2 + xy + y^2} } \)
\( \frac {2a} {a^3 + a^2 b - ab^2 - b^3} - \frac {1} {a^2 - b^2 } =\answer [onlineshowanswerbutton]{\frac {1}{(a + b)^2} } \)
\( \frac {1} {a^2 - a} - \frac {1} {a^2 + a} + \frac {2a^5}{a^2 - a^4 } =\answer [onlineshowanswerbutton]{\frac {-2(a^2 + 1)}{a} } \)
Bereken en vereenvoudig indien mogelijk.
\( \frac {x^2 - x} {x - 1} \cdot \frac {5x - 5} {1 - x } =\answer [onlineshowanswerbutton]{-5x } \)
\( \frac {x^3 - 8} {x^3 + 8} \cdot \frac {x^2 + 4x + 4} {x^2 - 4 } =\answer [onlineshowanswerbutton]{\frac {x^2 + 2x + 4}{x^2 - 2x + 4} } \)
\( \frac {xy + y^2} {(x - y)^2} \cdot \frac {x^2 - xy} {(x + y)^2 } =\answer [onlineshowanswerbutton]{\frac {xy}{x^2 - y^2} } \)
\( \frac {2a^2 + 2ab} {ab - b^2} \cdot \frac {a^2 - b^2} {a^2 + 2ab + b^2 } =\answer [onlineshowanswerbutton]{\frac {2a}{b} } \)
\( \frac {x^2 + 3x - 10} {2x} \cdot \frac {x^2 - 3x} {x^2 - 5x + 6 } =\answer [onlineshowanswerbutton]{\frac {1}{2}(x + 5) } \)
Bereken en vereenvoudig indien mogelijk.
\( \left ( 1 - \frac {1}{x - 2} \right ) \left ( x - 3 + \frac {1}{x - 3} \right ) =\answer [onlineshowanswerbutton]{\frac {x^2 - 6x + 10}{x - 2} } \)
\( \left ( x - \frac {x + 2}{x} \right ) \left ( 5 - \frac {1}{x + 1} \right ) =\answer [onlineshowanswerbutton]{\frac {(x - 2)(5x + 4)}{x} } \)
\( \left ( x - \frac {x - y}{1 + xy} \right ) \left ( x - \frac {2}{x + 1} \right ) =\answer [onlineshowanswerbutton]{\frac {(x^2 + 1)(x^2 + x - 2)y}{(x + 1)(xy + 1)}} \)
\( \left ( 3 - \frac {1}{a + 2} \right ) \left ( a + 1 + \frac {2a + 1}{a - 1} \right ) =\answer [onlineshowanswerbutton]{\frac {a(3a + 5)}{a - 1} } \)
\( \left ( \frac {b + a}{b + 2a} - \frac {b - a}{b - 2a} \right ) \left ( \frac {b^2}{a^2} - 4 \right ) =\answer [onlineshowanswerbutton]{\frac {-2b}{a} } \)
Bereken en vereenvoudig indien mogelijk.
\( \frac {\frac {5x^2 - 5}{x^2}} {\frac {6x + 6}{x^3}} =\answer [onlineshowanswerbutton]{\frac {5x(x - 1)}{6} } \)
\( \frac {\frac {x^2 + 5x + 6}{x^2 + 6x + 5}} {\frac {x^2 + 4x + 4}{x^2 + 7x + 10}} =\answer [onlineshowanswerbutton]{\frac {x + 3}{x + 1} } \)
\( \frac {3 + \frac {1}{x - 2}} {3 - \frac {1}{x - 5}} =\answer [onlineshowanswerbutton]{\frac {(x - 5)(3x - 5)}{(x - 2)(3x - 16)}} \)
\( \frac {x - \frac {1}{x}} {x + \frac {1}{x}} =\answer [onlineshowanswerbutton]{\frac {x^2 - 1}{x^2 + 1} } \)
\( \frac {\frac {1}{a - b} + 1} {\frac {1}{a - b} - 1} =\answer [onlineshowanswerbutton]{\frac {-(a - b + 1)}{a - b - 1} } \)
\( \frac {(x - 3)^2} {x} \div (x^2 - 9) =\answer [onlineshowanswerbutton]{\frac {x - 3}{x(x + 3)} } \)
\( \frac {5 + \frac {3}{x + 1}} {5} =\answer [onlineshowanswerbutton]{\frac {5x + 8}{5(x + 1)} } \)
\( \frac {x + 2} {\frac {3}{x + 4} - 2} =\answer [onlineshowanswerbutton]{\frac {-(x + 2)(x + 4)}{2x + 5} } \)
\( \frac {1} {\frac {1}{a} - \frac {1}{b}} \cdot \left ( \frac {b}{a} - \frac {a}{b} \right ) =\answer [onlineshowanswerbutton]{a + b } \)
\( \frac {1} {1 + \frac {4x^2}{(x^2 - 1)^2}} \cdot \frac {(x^2 + 1)^2}{(x - 1)^2} =\answer [onlineshowanswerbutton]{(x + 1)^2 } \)
Bereken en vereenvoudig indien mogelijk.
\( \left ( \frac {1}{a} + \frac {1}{b} \right )^{-1 }=\answer [onlineshowanswerbutton]{\frac {ab}{a + b} } \)
\( \left ( \frac {a}{a - b} - \frac {b}{b - a} \right )^{-1 }=\answer [onlineshowanswerbutton]{\frac {a - b}{a + b} } \)
\( \left ( y^{-2} - x^{-2} \right )\left ( \frac {1}{y} - \frac {1}{x} \right )^{-1}=\answer [onlineshowanswerbutton]{\frac {x + y}{xy} } \)
Bereken en vereenvoudig indien mogelijk.
\( \frac {(a - 1)^3 - (a + 1)(a - 1)^2}{(a - 1)^6} =\answer [onlineshowanswerbutton]{\frac {-2}{(a-1)^4} } \)
\( \frac {3x + 3}{x^2 - 2x} - \frac {2x + 2}{x^2 - 4} =\answer [onlineshowanswerbutton]{\frac {(x+1)(x+6)}{x(x^2-4)} } \)
\( \left ( \frac {1}{y^2} - \frac {1}{x^2} \right ) \cdot \frac {y}{1 - \frac {y}{x}} =\answer [onlineshowanswerbutton]{\frac {x + y}{xy} } \)
\( \frac {1 + t}{1 - t^2} + \frac {1 + t}{(1 - t)^2} =\answer [onlineshowanswerbutton]{\frac {2}{(1 - t)^2} } \)
\( \frac {x^2 - y^2 + x + y}{x + y} =\answer [onlineshowanswerbutton]{x - y + 1 } \)
\( \frac {1}{y} - y \) /
\( 1 - \frac {1}{y} =\answer [onlineshowanswerbutton]{-(y + 1) } \)
\( \frac {1 + x}{1 + 2x + x^2} - \frac {1 + x}{1 + x^3} =\answer [onlineshowanswerbutton]{\frac {x(x - 2)}{x^3 + 1} } \)
\( \frac {\frac {x^2 - 4}{(x - 2)^2}}{x + 2} =\answer [onlineshowanswerbutton]{\frac {1}{x - 2} } \)
\( \frac {x^2 - 4}{\frac {(x - 2)^2}{x + 2}} =\answer [onlineshowanswerbutton]{\frac {(x + 2)^2}{x - 2} } \)
\( \frac {1}{\frac {a - b}{ab}} \cdot \left ( \frac {b}{a} - \frac {a}{b} \right ) =\answer [onlineshowanswerbutton]{-(a + b) } \)
\( \frac {1}{a^2 - 2a} + 5 + \frac {6}{2 - a} =\answer [onlineshowanswerbutton]{\frac {5a^2 - 16a + 1}{a^2 - 2a} } \)
\( \frac {1}{\frac {1}{x} + \frac {1}{y}} =\answer [onlineshowanswerbutton]{\frac {xy}{x + y} } \)
\( \frac {x + 2y}{\frac {1}{x} - \frac {2}{y}} =\answer [onlineshowanswerbutton]{\frac {xy(x + 2y)}{y - 2x} } \)
\( \frac {(x - a)(x^2 + 2ax + a^2)}{x^3 + a^3} \cdot \frac {x^2 - ax + a^2}{x^3 - a^3} =\answer [onlineshowanswerbutton]{\frac {x + a}{x^2 + ax + a^2} } \)
\( \frac {x^3 - y^3}{x^4 - y^4} \cdot \frac {x^2 + y^2}{x^2 + xy + y^2} \cdot \frac {x - y}{(x + y)^2} =\answer [onlineshowanswerbutton]{\frac {x - y}{(x + y)^3} } \)
\( \left ( y^{-2} - x^{-2} \right ) \cdot \frac {y}{1 - yx^{-1}} =\answer [onlineshowanswerbutton]{\frac {x + y}{xy} } \)
\( \left ( 1 - \frac {1}{x} \right ) \left ( 2 - \frac {1}{x} \right ) \cdot \frac {1}{x^2 - 3x + 2} =\answer [onlineshowanswerbutton]{\frac {2x - 1}{x^2(x - 2)} } \)
\( \frac {2x + 3}{x^2 - 7x + 12} - \frac {2}{x - 3} =\answer [onlineshowanswerbutton]{\frac {11}{(x - 4)(x - 3)} } \)
\( \frac {2x^2 - x - 6}{\frac {4}{x^2} - 1} =\answer [onlineshowanswerbutton]{\frac {-x^2(2x + 3)}{x + 2} } \)
\( \frac {\frac {1}{x^2} - 1}{\frac {1}{x} - \frac {2}{x^2} - \frac {3}{x^3}} =\answer [onlineshowanswerbutton]{\frac {-x(x - 1)}{x - 3} } \)
