化简 (x-3)/(x^2+5x-24)*(x^2-64)/(7x-49)

解答

化简

\frac{x - 3}{x ^{2} + 5 x - 24} \cdot \frac{x ^{2} - 64}{7 x - 49}

\frac{x - 8}{7 x - 49}

求解步骤

\frac{x - 3}{x ^{2} + 5 x - 24} \cdot \frac{x ^{2} - 64}{7 x - 49}

消掉

\frac{x - 3}{x ^{2} + 5 x - 24} : \frac{1}{x + 8}

= \frac{1}{x + 8} \cdot \frac{x ^{2} - 64}{7 x - 49}

使用分式法则:

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

= \frac{1 \cdot ( x ^{2} - 64 )}{( x + 8 ) ( 7 x - 49 )}

使用法则:

1 \cdot a = a

1 \cdot (x^{2} - 64) = (x^{2} - 64)

= \frac{x ^{2} - 64}{( x + 8 ) ( 7 x - 49 )}

因式分解

x^{2} - 64 : (x + 8) (x - 8)

= \frac{( x + 8 ) ( x - 8 )}{( x + 8 ) ( 7 x - 49 )}

约分:

x + 8

= \frac{x - 8}{7 x - 49}

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