Solve 81-a^2/a^2+6a+9div9-a/2a+6*1/a+9

$$\frac { 81 - a ^ { 2 } } { a ^ { 2 } + 6 a + 9 } \div \frac { 9 - a } { 2 a + 6 } \cdot \frac { 1 } { a + 9 }$$

Evaluate

$$\frac{2}{a+3}$$

Short Solution Steps

Divide \frac{81-a^{2}}{a^{2}+6a+9} by \frac{9-a}{2a+6} by multiplying \frac{81-a^{2}}{a^{2}+6a+9} by the reciprocal of \frac{9-a}{2a+6}.

$$\frac{\left(81-a^{2}\right)\left(2a+6\right)}{\left(a^{2}+6a+9\right)\left(9-a\right)}\times \frac{1}{a+9}$$

Factor the expressions that are not already factored in \frac{\left(81-a^{2}\right)\left(2a+6\right)}{\left(a^{2}+6a+9\right)\left(9-a\right)}.

$$\frac{2\left(a-9\right)\left(-a-9\right)\left(a+3\right)}{\left(-a+9\right)\left(a+3\right)^{2}}\times \frac{1}{a+9}$$

Extract the negative sign in -9+a.

$$\frac{-2\left(-a-9\right)\left(a+3\right)\left(-a+9\right)}{\left(-a+9\right)\left(a+3\right)^{2}}\times \frac{1}{a+9}$$

Cancel out \left(a+3\right)\left(-a+9\right) in both numerator and denominator.

$$\frac{-2\left(-a-9\right)}{a+3}\times \frac{1}{a+9}$$

Multiply \frac{-2\left(-a-9\right)}{a+3} times \frac{1}{a+9} by multiplying numerator times numerator and denominator times denominator.

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

Extract the negative sign in -a-9.

$$\frac{-2\left(-1\right)\left(a+9\right)}{\left(a+3\right)\left(a+9\right)}$$

Cancel out a+9 in both numerator and denominator.

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

Multiply -2 and -1 to get 2.

$$\frac{2}{a+3}$$

Expand

$$\frac{2}{a+3}$$

Short Solution Steps

Divide \frac{81-a^{2}}{a^{2}+6a+9} by \frac{9-a}{2a+6} by multiplying \frac{81-a^{2}}{a^{2}+6a+9} by the reciprocal of \frac{9-a}{2a+6}.

$$\frac{\left(81-a^{2}\right)\left(2a+6\right)}{\left(a^{2}+6a+9\right)\left(9-a\right)}\times \frac{1}{a+9}$$

Factor the expressions that are not already factored in \frac{\left(81-a^{2}\right)\left(2a+6\right)}{\left(a^{2}+6a+9\right)\left(9-a\right)}.

$$\frac{2\left(a-9\right)\left(-a-9\right)\left(a+3\right)}{\left(-a+9\right)\left(a+3\right)^{2}}\times \frac{1}{a+9}$$

Extract the negative sign in -9+a.

$$\frac{-2\left(-a-9\right)\left(a+3\right)\left(-a+9\right)}{\left(-a+9\right)\left(a+3\right)^{2}}\times \frac{1}{a+9}$$

Cancel out \left(a+3\right)\left(-a+9\right) in both numerator and denominator.

$$\frac{-2\left(-a-9\right)}{a+3}\times \frac{1}{a+9}$$

Multiply \frac{-2\left(-a-9\right)}{a+3} times \frac{1}{a+9} by multiplying numerator times numerator and denominator times denominator.

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

Extract the negative sign in -a-9.

$$\frac{-2\left(-1\right)\left(a+9\right)}{\left(a+3\right)\left(a+9\right)}$$

Cancel out a+9 in both numerator and denominator.

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

Multiply -2 and -1 to get 2.

$$\frac{2}{a+3}$$