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\frac{\left(x-1\right)^2\left(2x-2\right)-2\left(x^2-2x-3\right)\left(x-1\right)}{\left(x-1\right)^4}

Solve ((x-1)^2(2x-2)(-2x-3+x^2)(x-1)*-2)/((x-1)^4)

Answer

$\frac{\left(x-1\right)^22\left(x-1\right)-2\left(x-1\right)\left(1+x\right)\left(x-3\right)}{\left(x-1\right)^4}$

Step-by-step explanation

Problem

$\frac{\left(x-1\right)^2\left(2x-2\right)-2\left(x^2-2x-3\right)\left(x-1\right)}{\left(x-1\right)^4}$
1

Factor the trinomial $\left(-3-2x+x^2\right)$ finding two numbers that multiply to form $-3$ and added form $-2$

$\begin{matrix}\left(-3\right)\left(1\right)=-3\\ \left(-3\right)+\left(1\right)=-2\end{matrix}$

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Answer

$\frac{\left(x-1\right)^22\left(x-1\right)-2\left(x-1\right)\left(1+x\right)\left(x-3\right)}{\left(x-1\right)^4}$

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