1
Solved example of algebraic fractions
$\frac{\left(1-x^2\right)^2}{x^2+2x+1}$
2
The trinomial $x^2+2x+1$ is a perfect square trinomial, because it's discriminant is equal to zero
$\Delta=b^2-4ac=2^2-4\left(1\right)\left(1\right) = 0$
3
Using the perfect square trinomial formula
$a^2+2ab+b^2=(a+b)^2,\:where\:a=\sqrt{x^2}\:and\:b=\sqrt{1}$
4
Factoring the perfect square trinomial
$\frac{\left(1-x^2\right)^2}{\left(x+1\right)^{2}}$
Intermediate steps
The power of a product is equal to the product of it's factors raised to the same power
$\frac{\left(1+x\right)^2\left(1-x\right)^2}{\left(x+1\right)^{2}}$
5
Factor the difference of squares $\left(1-x^2\right)$ as the product of two conjugated binomials
$\frac{\left(1+x\right)^2\left(1-x\right)^2}{\left(x+1\right)^{2}}$
6
Simplify the fraction $\frac{\left(1+x\right)^2\left(1-x\right)^2}{\left(x+1\right)^{2}}$ by $\left(1+x\right)^2$
$\left(1-x\right)^2$
Final Answer
$\left(1-x\right)^2$
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