expand ((x-1)(x+3)(x-5))/((x+2)^2(x-4))

الحلّ

expand

\frac{( x - 1 ) ( x + 3 ) ( x - 5 )}{( x + 2 ) ^{2} ( x - 4 )}

\frac{x ^{3} - 3 x ^{2} - 13 x + 15}{x ^{3} - 12 x - 16}

خطوات الحلّ

\frac{( x - 1 ) ( x + 3 ) ( x - 5 )}{( x + 2 ) ^{2} ( x - 4 )}

(x + 2)^{2} = x^{2} + 4 x + 4

= \frac{( x - 1 ) ( x + 3 ) ( x - 5 )}{( x ^{2} + 4 x + 4 ) ( x - 4 )}

(x^{2} + 4 x + 4) (x - 4)

وسٌع:

x^{3} - 12 x - 16

= \frac{( x - 1 ) ( x + 3 ) ( x - 5 )}{x ^{3} - 12 x - 16}

(x - 1) (x + 3) (x - 5)

وسٌع:

x^{3} - 3 x^{2} - 13 x + 15

= \frac{x ^{3} - 3 x ^{2} - 13 x + 15}{x ^{3} - 12 x - 16}

(x + 52) (x - 52)

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

(x - 1) (x - \frac{3}{2})

(sec (x) + tan (x)) (sin (x) - 1)

(5 - 4 i)^{4}