化简 7/(2x^2+18x)-(5x)/(x^2+17x+72)

解答

化简

\frac{7}{2 x ^{2} + 18 x} - \frac{5 x}{x ^{2} + 17 x + 72}

\frac{7 x + 56 - 10 x ^{2}}{2 x ( x + 9 ) ( x + 8 )}

求解步骤

\frac{7}{2 x ^{2} + 18 x} - \frac{5 x}{x ^{2} + 17 x + 72}

2 x^{2} + 18 x, x^{2} + 17 x + 72

的最小公倍数:

2 x (x + 9) (x + 8)

根据最小公倍数调整分式

= \frac{7 ( x + 8 )}{2 x ( x + 9 ) ( x + 8 )} - \frac{10 x ^{2}}{2 x ( x + 9 ) ( x + 8 )}

使用分式法则:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{7 ( x + 8 ) - 10 x ^{2}}{2 x ( x + 9 ) ( x + 8 )}

化简

7 (x + 8) - 10 x^{2} : 7 x + 56 - 10 x^{2}

= \frac{7 x + 56 - 10 x ^{2}}{2 x ( x + 9 ) ( x + 8 )}

s im pl i f y \frac{\frac{7}{6 x}}{\frac{7}{12 x}}

f a c t or 2 + x - x^{2}

s im pl i f y (x^{7})^{3}

s im pl i f y 2 - 5 \cdot 2 + 6^{2} + 9 - 2^{3}

s im pl i f y \frac{3}{2 - 5}