Solve a^2-a-6/a^2-4+a^2+2a-7/a-2

$$\frac { a ^ { 2 } - a - 6 } { a ^ { 2 } - 4 } + \frac { a ^ { 2 } + 2 a - 7 } { a - 2 }$$

Evaluate

$$a+5$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-a-6}{a^{2}-4}.

$$\frac{\left(a-3\right)\left(a+2\right)}{\left(a-2\right)\left(a+2\right)}+\frac{a^{2}+2a-7}{a-2}$$

Cancel out a+2 in both numerator and denominator.

$$\frac{a-3}{a-2}+\frac{a^{2}+2a-7}{a-2}$$

Since \frac{a-3}{a-2} and \frac{a^{2}+2a-7}{a-2} have the same denominator, add them by adding their numerators.

$$\frac{a-3+a^{2}+2a-7}{a-2}$$

Combine like terms in a-3+a^{2}+2a-7.

$$\frac{3a-10+a^{2}}{a-2}$$

Factor the expressions that are not already factored in \frac{3a-10+a^{2}}{a-2}.

$$\frac{\left(a-2\right)\left(a+5\right)}{a-2}$$

Cancel out a-2 in both numerator and denominator.

$$a+5$$

Expand

$$a+5$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-a-6}{a^{2}-4}.

$$\frac{\left(a-3\right)\left(a+2\right)}{\left(a-2\right)\left(a+2\right)}+\frac{a^{2}+2a-7}{a-2}$$

Cancel out a+2 in both numerator and denominator.

$$\frac{a-3}{a-2}+\frac{a^{2}+2a-7}{a-2}$$

Since \frac{a-3}{a-2} and \frac{a^{2}+2a-7}{a-2} have the same denominator, add them by adding their numerators.

$$\frac{a-3+a^{2}+2a-7}{a-2}$$

Combine like terms in a-3+a^{2}+2a-7.

$$\frac{3a-10+a^{2}}{a-2}$$

Factor the expressions that are not already factored in \frac{3a-10+a^{2}}{a-2}.

$$\frac{\left(a-2\right)\left(a+5\right)}{a-2}$$

Cancel out a-2 in both numerator and denominator.

$$a+5$$