化简 9/(x^2-12x+36)+x/(x^2-36)

解答

化简

\frac{9}{x ^{2} - 12 x + 36} + \frac{x}{x ^{2} - 36}

\frac{x ^{2} + 3 x + 54}{( x - 6 ) ^{2} ( x + 6 )}

求解步骤

\frac{9}{x ^{2} - 12 x + 36} + \frac{x}{x ^{2} - 36}

x^{2} - 12 x + 36, x^{2} - 36

的最小公倍数:

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

根据最小公倍数调整分式

= \frac{9 ( x + 6 )}{( x - 6 ) ^{2} ( x + 6 )} + \frac{x ( x - 6 )}{( x - 6 ) ^{2} ( x + 6 )}

使用分式法则:

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

= \frac{9 ( x + 6 ) + x ( x - 6 )}{( x - 6 ) ^{2} ( x + 6 )}

化简

9 (x + 6) + x (x - 6) : x^{2} + 3 x + 54

= \frac{x ^{2} + 3 x + 54}{( x - 6 ) ^{2} ( x + 6 )}

f a c t or 125 a^{3} + 1

s im pl i f y \frac{d - 2}{d ^{2} - 4} + \frac{4}{d ^{2} + 4 d + 4}

s im pl i f y \frac{\frac{1}{x ^{2}}}{\frac{1}{x}}

s im pl i f y \frac{3 ^{9}}{3 ^{- 5}}

f a c t or x^{3} + 12 x