Solve (1+1/a+2)diva^2-9/a+2

$$( 1 + \frac { 1 } { a + 2 } ) \div \frac { a ^ { 2 } - 9 } { a + 2 }$$

Evaluate

$$\frac{1}{a-3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a+2}{a+2}.

$$\frac{\frac{a+2}{a+2}+\frac{1}{a+2}}{\frac{a^{2}-9}{a+2}}$$

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

$$\frac{\frac{a+2+1}{a+2}}{\frac{a^{2}-9}{a+2}}$$

Combine like terms in a+2+1.

$$\frac{\frac{a+3}{a+2}}{\frac{a^{2}-9}{a+2}}$$

Divide \frac{a+3}{a+2} by \frac{a^{2}-9}{a+2} by multiplying \frac{a+3}{a+2} by the reciprocal of \frac{a^{2}-9}{a+2}.

$$\frac{\left(a+3\right)\left(a+2\right)}{\left(a+2\right)\left(a^{2}-9\right)}$$

Cancel out a+2 in both numerator and denominator.

$$\frac{a+3}{a^{2}-9}$$

Factor the expressions that are not already factored.

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

Cancel out a+3 in both numerator and denominator.

$$\frac{1}{a-3}$$

Expand

$$\frac{1}{a-3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a+2}{a+2}.

$$\frac{\frac{a+2}{a+2}+\frac{1}{a+2}}{\frac{a^{2}-9}{a+2}}$$

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

$$\frac{\frac{a+2+1}{a+2}}{\frac{a^{2}-9}{a+2}}$$

Combine like terms in a+2+1.

$$\frac{\frac{a+3}{a+2}}{\frac{a^{2}-9}{a+2}}$$

Divide \frac{a+3}{a+2} by \frac{a^{2}-9}{a+2} by multiplying \frac{a+3}{a+2} by the reciprocal of \frac{a^{2}-9}{a+2}.

$$\frac{\left(a+3\right)\left(a+2\right)}{\left(a+2\right)\left(a^{2}-9\right)}$$

Cancel out a+2 in both numerator and denominator.

$$\frac{a+3}{a^{2}-9}$$

Factor the expressions that are not already factored.

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

Cancel out a+3 in both numerator and denominator.

$$\frac{1}{a-3}$$