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受欢迎的代数 >

化简 (5x-10)/(x^2-36)*(4x+24)/(x^2+5x-14)

解答

化简

\frac{5 x - 10}{x ^{2} - 36} \cdot \frac{4 x + 24}{x ^{2} + 5 x - 14}

解答

\frac{20}{( x - 6 ) ( x + 7 )}

求解步骤

\frac{5 x - 10}{x ^{2} - 36} \cdot \frac{4 x + 24}{x ^{2} + 5 x - 14}

使用分式法则:

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

= \frac{( 5 x - 10 ) ( 4 x + 24 )}{( x ^{2} - 36 ) ( x ^{2} + 5 x - 14 )}

因式分解

5 x - 10 : 5 (x - 2)

= \frac{5 ( x - 2 ) ( 4 x + 24 )}{( x ^{2} - 36 ) ( x ^{2} + 5 x - 14 )}

因式分解

x^{2} + 5 x - 14 : (x - 2) (x + 7)

= \frac{5 ( x - 2 ) ( 4 x + 24 )}{( x ^{2} - 36 ) ( x - 2 ) ( x + 7 )}

约分:

x - 2

= \frac{5 ( 4 x + 24 )}{( x ^{2} - 36 ) ( x + 7 )}

因式分解

4 x + 24 : 4 (x + 6)

= \frac{5 \cdot 4 ( x + 6 )}{( x ^{2} - 36 ) ( x + 7 )}

因式分解

x^{2} - 36 : (x + 6) (x - 6)

= \frac{5 \cdot 4 ( x + 6 )}{( x + 6 ) ( x - 6 ) ( x + 7 )}

约分:

x + 6

= \frac{5 \cdot 4}{( x - 6 ) ( x + 7 )}

数字相乘:

5 \cdot 4 = 20

= \frac{20}{( x - 6 ) ( x + 7 )}

流行的例子

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s im pl i f y \frac{32}{25}

s im pl i f y (x + 3) + 3

s im pl i f y \frac{- 11}{2}

s im pl i f y - 2 (x + 5)

化简 (10x^2-10x+2)-(-8x^2+7x-7)

s im pl i f y (10 x^{2} - 10 x + 2) - (- 8 x^{2} + 7 x - 7)