化简 (14)/((x^2-4))-((6-x))/((x+2))

解答

化简

\frac{14}{( x ^{2} - 4 )} - \frac{( 6 - x )}{( x + 2 )}

\frac{x ^{2} - 8 x + 26}{( x + 2 ) ( x - 2 )}

求解步骤

\frac{14}{x ^{2} - 4} - \frac{6 - x}{x + 2}

x^{2} - 4, x + 2

的最小公倍数:

(x + 2) (x - 2)

根据最小公倍数调整分式

= \frac{14}{( x + 2 ) ( x - 2 )} - \frac{( 6 - x ) ( x - 2 )}{( x + 2 ) ( x - 2 )}

使用分式法则:

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

= \frac{14 - ( 6 - x ) ( x - 2 )}{( x + 2 ) ( x - 2 )}

化简

14 - (6 - x) (x - 2) : x^{2} - 8 x + 26

= \frac{x ^{2} - 8 x + 26}{( x + 2 ) ( x - 2 )}

s im pl i f y (2 x)^{2} (x - x^{2}) - 4 x (- x^{3} + x^{2} - 5)

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