Solve (x + 1)/(x - 1) + (x ^ 2 - 1)/(x + 1) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{x+1}{x-1}+\frac{x^{2}-1}{x+1}$$

Evaluate

$\frac{x^{2}-x+2}{x-1}$

Short Solution Steps

Factor the expressions that are not already factored in $\frac{x^{2}-1}{x+1}$.

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

Cancel out $x+1$ in both numerator and denominator.

$$\frac{x+1}{x-1}+x-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $x-1$ times $\frac{x-1}{x-1}$.

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

Since $\frac{x+1}{x-1}$ and $\frac{\left(x-1\right)\left(x-1\right)}{x-1}$ have the same denominator, add them by adding their numerators.

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

Do the multiplications in $x+1+\left(x-1\right)\left(x-1\right)$.

$$\frac{x+1+x^{2}-x-x+1}{x-1}$$

Combine like terms in $x+1+x^{2}-x-x+1$.

$$\frac{-x+2+x^{2}}{x-1}$$

Expand

$\frac{x^{2}-x+2}{x-1}$

Short Solution Steps

Factor the expressions that are not already factored in $\frac{x^{2}-1}{x+1}$.

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

Cancel out $x+1$ in both numerator and denominator.

$$\frac{x+1}{x-1}+x-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $x-1$ times $\frac{x-1}{x-1}$.

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

Since $\frac{x+1}{x-1}$ and $\frac{\left(x-1\right)\left(x-1\right)}{x-1}$ have the same denominator, add them by adding their numerators.

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

Do the multiplications in $x+1+\left(x-1\right)\left(x-1\right)$.

$$\frac{x+1+x^{2}-x-x+1}{x-1}$$

Combine like terms in $x+1+x^{2}-x-x+1$.

$$\frac{-x+2+x^{2}}{x-1}$$