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Step-by-step Solution

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

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Answer

$\frac{-2\left(x-1\right)^2-6+x2\left(-x^{2}+\left(x-1\right)^2\right)+x2\left(x-2\right)+x2\left(2x+3\right)}{\left(x-1\right)^4}$

Step-by-step explanation

Problem to solve:

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

Multiplying polynomials $-3$ and $-2x+2$

$\frac{2\left(x-1\right)^2x-2\left(x-1\right)^2-2x^{3}+2x^2+4x^2-4x+6x-6}{\left(x-1\right)^4}$
2

Factoring by $x$

$\frac{-2\left(x-1\right)^2-6+x\left(-2x^{2}+2\left(x-1\right)^2\right)+x\left(2x-4\right)+x\left(4x+6\right)}{\left(x-1\right)^4}$

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Answer

$\frac{-2\left(x-1\right)^2-6+x2\left(-x^{2}+\left(x-1\right)^2\right)+x2\left(x-2\right)+x2\left(2x+3\right)}{\left(x-1\right)^4}$

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

Main topic:

Polynomials

Time to solve it:

~ 0.93 seconds