Solve 2a+2/a-1div(a+1)-a^2-1/a^2-2a+1

$$\frac { 2 a + 2 } { a - 1 } \div ( a + 1 ) - \frac { a ^ { 2 } - 1 } { a ^ { 2 } - 2 a + 1 }$$

Evaluate

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Short Solution Steps

Express \frac{\frac{2a+2}{a-1}}{a+1} as a single fraction.

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

Factor the expressions that are not already factored in \frac{2a+2}{\left(a-1\right)\left(a+1\right)}.

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

Cancel out a+1 in both numerator and denominator.

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

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

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

Cancel out a-1 in both numerator and denominator.

$$\frac{2}{a-1}-\frac{a+1}{a-1}$$

Since \frac{2}{a-1} and \frac{a+1}{a-1} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-\left(a+1\right)}{a-1}$$

Do the multiplications in 2-\left(a+1\right).

$$\frac{2-a-1}{a-1}$$

Combine like terms in 2-a-1.

$$\frac{1-a}{a-1}$$

Extract the negative sign in 1-a.

$$\frac{-\left(a-1\right)}{a-1}$$

Cancel out a-1 in both numerator and denominator.

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Factor

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