Solve frac{a^{2}-a-2}{a+3}*a^2+2a-3/(a-2)^3*(a-2)^2/a^2-1=

$$\frac { a ^ { 2 } - a - 2 } { a + 3 } \cdot \frac { a ^ { 2 } + 2 a - 3 } { ( a - 2 ) ^ { 3 } } \cdot \frac { ( a - 2 ) ^ { 2 } } { a ^ { 2 } - 1 } =$$

Evaluate

$$1$$

Short Solution Steps

Multiply \frac{a^{2}-a-2}{a+3} times \frac{a^{2}+2a-3}{\left(a-2\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

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

Multiply \frac{\left(a^{2}-a-2\right)\left(a^{2}+2a-3\right)}{\left(a+3\right)\left(a-2\right)^{3}} times \frac{\left(a-2\right)^{2}}{a^{2}-1} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out \left(a-2\right)^{2} in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out \left(a-2\right)\left(a-1\right)\left(a+1\right)\left(a+3\right) in both numerator and denominator.

$$1$$

Factor

$$1$$