化简 (\frac{x^2+9x+18)/(x^2+6x+8)}{(x^2-3x-18)/(x^2+2x-8)}

解答

化简

\frac{\frac{x ^{2} + 9 x + 18}{x ^{2} + 6 x + 8}}{\frac{x ^{2} - 3 x - 18}{x ^{2} + 2 x - 8}}

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

求解步骤

\frac{\frac{x ^{2} + 9 x + 18}{x ^{2} + 6 x + 8}}{\frac{x ^{2} - 3 x - 18}{x ^{2} + 2 x - 8}}

使用分式法则:

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

= \frac{( x ^{2} + 9 x + 18 ) ( x ^{2} + 2 x - 8 )}{( x ^{2} + 6 x + 8 ) ( x ^{2} - 3 x - 18 )}

消掉

\frac{( x ^{2} + 9 x + 18 ) ( x ^{2} + 2 x - 8 )}{( x ^{2} + 6 x + 8 ) ( x ^{2} - 3 x - 18 )} : \frac{( x + 6 ) ( x - 2 )}{( x + 2 ) ( x - 6 )}

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

s im pl i f y \frac{3 a ^{3} - 75 a}{a ( a + 5 ) ( a + 5 )}

f a c t or 36 n^{2} - 1

s im pl i f y \frac{x ^{2} - 4}{x ^{2} - 6 x + 8}

s im pl i f y sec^{4} (x) - sec^{2} (x)

e x p an d (6 ab + 10) (7 a - 2 b)