Solve -a+2/a-1*2a^2-4a/a^2-4diva/a^2-1

$$\frac { - a + 2 } { a - 1 } \cdot \frac { 2 a ^ { 2 } - 4 a } { a ^ { 2 } - 4 } \div \frac { a } { a ^ { 2 } - 1 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{2a^{2}-4a}{a^{2}-4}.

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

Cancel out a-2 in both numerator and denominator.

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

Multiply \frac{-a+2}{a-1} times \frac{2a}{a+2} by multiplying numerator times numerator and denominator times denominator.

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

Divide \frac{\left(-a+2\right)\times 2a}{\left(a-1\right)\left(a+2\right)} by \frac{a}{a^{2}-1} by multiplying \frac{\left(-a+2\right)\times 2a}{\left(a-1\right)\left(a+2\right)} by the reciprocal of \frac{a}{a^{2}-1}.

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-1 in both numerator and denominator.

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

Expand the expression.

$$\frac{-2a^{2}+2a+4}{a+2}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{2a^{2}-4a}{a^{2}-4}.

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

Cancel out a-2 in both numerator and denominator.

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

Multiply \frac{-a+2}{a-1} times \frac{2a}{a+2} by multiplying numerator times numerator and denominator times denominator.

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

Divide \frac{\left(-a+2\right)\times 2a}{\left(a-1\right)\left(a+2\right)} by \frac{a}{a^{2}-1} by multiplying \frac{\left(-a+2\right)\times 2a}{\left(a-1\right)\left(a+2\right)} by the reciprocal of \frac{a}{a^{2}-1}.

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a-1 in both numerator and denominator.

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

Expand the expression.

$$\frac{-2a^{2}+2a+4}{a+2}$$