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

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Solution

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Final Answer

$\frac{2\left(\left(x-1\right)^2-x^2+2x+3\right)}{\left(x-1\right)^{3}}$
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Step-by-step Solution

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Factor the polynomial $\left(x-1\right)^2\left(2x-2\right)-2\left(x^2-2x-3\right)\left(x-1\right)$ by it's greatest common factor (GCF): $x-1$

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

Learn how to solve simplification of algebraic fractions problems step by step online.

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

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Learn how to solve simplification of algebraic fractions problems step by step online. Simplify the expression ((x-1)^2(2x-2)-2(x^2-2x+-3)(x-1))/((x-1)^4). Factor the polynomial \left(x-1\right)^2\left(2x-2\right)-2\left(x^2-2x-3\right)\left(x-1\right) by it's greatest common factor (GCF): x-1. Simplify the fraction by x-1. Factor \left(x-1\right)\left(2x-2\right)-2x^2+4x+6 by the greatest common divisor 2. Factor \left(2x-2\right) by the greatest common divisor 2.

Final Answer

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

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind ((x-1)^2(2x-2)+-2(x^2+-2x))/((x-1)^4) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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

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(◻)
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◻/◻
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÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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