展开 3/(x+5)+7/(x-2)

解答

展开

\frac{3}{x + 5} + \frac{7}{x - 2}

\frac{10 x + 29}{x ^{2} + 3 x - 10}

求解步骤

\frac{3}{x + 5} + \frac{7}{x - 2}

x + 5, x - 2

的最小公倍数:

(x + 5) (x - 2)

根据最小公倍数调整分式

= \frac{3 ( x - 2 )}{( x + 5 ) ( x - 2 )} + \frac{7 ( x + 5 )}{( x - 2 ) ( x + 5 )}

因为分母相等，所以合并分式:

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

= \frac{3 ( x - 2 ) + 7 ( x + 5 )}{( x + 5 ) ( x - 2 )}

乘开

(x + 5) (x - 2) : x^{2} + 3 x - 10

= \frac{3 ( x - 2 ) + 7 ( x + 5 )}{x ^{2} + 3 x - 10}

乘开

3 (x - 2) + 7 (x + 5) : 10 x + 29

= \frac{10 x + 29}{x ^{2} + 3 x - 10}

e x p an d 18 ((x - 1)^{3} (x - 3)^{11})

e x p an d (6 x y^{3} + cos (y)) d x + (3 k x^{2} y^{2} - 3 y^{2}) d y

e x p an d f (15 x^{4} - 33 x^{2} + 4) d x

e x p an d \frac{s + 6}{( s - 1 ) ( s - 2 ) ^{2}}

e x p an d \frac{( 2 x + 1 ) ( x - 9 )}{x + 7}