化简 (x^2-x-30)/(5x+40)*(3x+6)/(x^2+7x+10)

解答

化简

\frac{x ^{2} - x - 30}{5 x + 40} \cdot \frac{3 x + 6}{x ^{2} + 7 x + 10}

\frac{3 ( x - 6 )}{5 x + 40}

求解步骤

\frac{x ^{2} - x - 30}{5 x + 40} \cdot \frac{3 x + 6}{x ^{2} + 7 x + 10}

消掉

\frac{3 x + 6}{x ^{2} + 7 x + 10} : \frac{3}{x + 5}

= \frac{x ^{2} - x - 30}{5 x + 40} \cdot \frac{3}{x + 5}

使用分式法则:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( x ^{2} - x - 30 ) \cdot 3}{( 5 x + 40 ) ( x + 5 )}

因式分解

x^{2} - x - 30 : (x + 5) (x - 6)

= \frac{( x + 5 ) ( x - 6 ) \cdot 3}{( 5 x + 40 ) ( x + 5 )}

约分:

x + 5

= \frac{( x - 6 ) \cdot 3}{5 x + 40}

= \frac{3 ( x - 6 )}{5 x + 40}

s im pl i f y \frac{2}{5} \times \frac{1}{4}

e x p an d (m + 6) (m - 6)

s im pl i f y \frac{( x ^{3} + 8 )}{( x + 2 )}

e x p an d (7 a^{2} - b) (3 a - 2 b)

s im pl i f y \frac{3 x + 18}{x ^{2} + 6 x}