What is expand (2x-1)/((ax+b)(cx+d)^2) ?

The solution to expand (2x-1)/((ax+b)(cx+d)^2) is (2x-1)/(ac^2x^3+2acdx^2+ad^2x+bc^2x^2+2bcdx+bd^2)

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expand (2x-1)/((ax+b)(cx+d)^2)

expand

\frac{2 x - 1}{( a x + b ) ( c x + d ) ^{2}}

\frac{2 x - 1}{a c ^{2} x ^{3} + 2 a c d x ^{2} + a d ^{2} x + b c ^{2} x ^{2} + 2 b c d x + b d ^{2}}

Solution steps

\frac{2 x - 1}{( a x + b ) ( c x + d ) ^{2}}

(c x + d)^{2} = c^{2} x^{2} + 2 c d x + d^{2}

= \frac{2 x - 1}{( a x + b ) ( c ^{2} x ^{2} + 2 c d x + d ^{2} )}

Expand

(a x + b) (c^{2} x^{2} + 2 c d x + d^{2}) : a c^{2} x^{3} + 2 a c d x^{2} + a d^{2} x + b c^{2} x^{2} + 2 b c d x + b d^{2}

= \frac{2 x - 1}{a c ^{2} x ^{3} + 2 a c d x ^{2} + a d ^{2} x + b c ^{2} x ^{2} + 2 b c d x + b d ^{2}}

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

\frac{2 ( x + 9 ) ( x - 1 )}{( x + 4 ) ( x - 2 )}

\frac{1}{( x + 1 ) ( x - 4 )}

- (u - z u) (z d u + u d z)

(2 - i)^{7}

What is expand (2x-1)/((ax+b)(cx+d)^2) ?
The solution to expand (2x-1)/((ax+b)(cx+d)^2) is (2x-1)/(ac^2x^3+2acdx^2+ad^2x+bc^2x^2+2bcdx+bd^2)