Question

simplify the given algebraic rational expression​

Answer 1

Answer:

$\frac{\left(x+5\right)}{\left(x+1\right)}$ is the simplified version of $\frac{2}{x+1}+\frac{2x}{x-1}+\frac{\left(x^2+3\right)}{1-x^2}$ ( PROVEN BELOW)

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Step-by-step explanation:

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

$=\frac{\left(-x^4-4x^3+6x^2+4x\ -\ 5\right)}{-x^4+2x^2-1}$

$=\frac{\left(-x-1\right)\left(x-1\right)\left(x-1\right)\left(x+5\right)}{\left(-x-1\right)\left(x-1\right)\left(x+1\right)\left(x-1\right)}$

$=\frac{\left(x+5\right)}{\left(x+1\right)}$