Solve a^2-9/a(a+3)^2+6/a(a+3)

$$\frac { a ^ { 2 } - 9 } { a ( a + 3 ) ^ { 2 } } + \frac { 6 } { a ( a + 3 ) }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-9}{a\left(a+3\right)^{2}}.

$$\frac{\left(a-3\right)\left(a+3\right)}{a\left(a+3\right)^{2}}+\frac{6}{a\left(a+3\right)}$$

Cancel out a+3 in both numerator and denominator.

$$\frac{a-3}{a\left(a+3\right)}+\frac{6}{a\left(a+3\right)}$$

Since \frac{a-3}{a\left(a+3\right)} and \frac{6}{a\left(a+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{a-3+6}{a\left(a+3\right)}$$

Combine like terms in a-3+6.

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

Cancel out a+3 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-9}{a\left(a+3\right)^{2}}.

$$\frac{\left(a-3\right)\left(a+3\right)}{a\left(a+3\right)^{2}}+\frac{6}{a\left(a+3\right)}$$

Cancel out a+3 in both numerator and denominator.

$$\frac{a-3}{a\left(a+3\right)}+\frac{6}{a\left(a+3\right)}$$

Since \frac{a-3}{a\left(a+3\right)} and \frac{6}{a\left(a+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{a-3+6}{a\left(a+3\right)}$$

Combine like terms in a-3+6.

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

Cancel out a+3 in both numerator and denominator.

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