What is expand (a(x+1)^2+b(x)(x+1)+cx)/(x(x+1)^2) ?

The solution to expand (a(x+1)^2+b(x)(x+1)+cx)/(x(x+1)^2) is (ax^2+2ax+a+bx^2+bx+cx)/(x^3+2x^2+x)

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expand (a(x+1)^2+b(x)(x+1)+cx)/(x(x+1)^2)

expand

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

(x + 1)^{2} = x^{2} + 2 x + 1

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

(x + 1)^{2} = x^{2} + 2 x + 1

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

Expand

x (x^{2} + 2 x + 1) : x^{3} + 2 x^{2} + x

= \frac{a ( x ^{2} + 2 x + 1 ) + b x ( x + 1 ) + c x}{x ^{3} + 2 x ^{2} + x}

Expand

a (x^{2} + 2 x + 1) + b x (x + 1) + c x : a x^{2} + 2 a x + a + b x^{2} + b x + c x

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

\frac{2 + v}{( v + 1 ) ( v + 4 )}

sin (x (π - \frac{π}{2 ^{x}}))

4 sin (\frac{π}{4} (x - 3)) + 6

\frac{1}{4} (\frac{1}{2} e^{2 x} - \frac{1}{2} e^{- 2 x})

\frac{( - z - 1 ) ^{3} z}{6}

What is expand (a(x+1)^2+b(x)(x+1)+cx)/(x(x+1)^2) ?
The solution to expand (a(x+1)^2+b(x)(x+1)+cx)/(x(x+1)^2) is (ax^2+2ax+a+bx^2+bx+cx)/(x^3+2x^2+x)