Solve 1/frac{n^2-6n+9{n+3}}{n+3/2n^2-18}

$$\frac { 1 } { \frac { n ^ { 2 } - 6 n + 9 } { n + 3 } } { \frac { n + 3 } { 2 n ^ { 2 } - 18 } }$$

Evaluate

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

Short Solution Steps

Divide 1 by \frac{n^{2}-6n+9}{n+3} by multiplying 1 by the reciprocal of \frac{n^{2}-6n+9}{n+3}.

$$\frac{n+3}{n^{2}-6n+9}\times \frac{n+3}{2n^{2}-18}$$

Factor the expressions that are not already factored in \frac{n+3}{2n^{2}-18}.

$$\frac{n+3}{n^{2}-6n+9}\times \frac{n+3}{2\left(n-3\right)\left(n+3\right)}$$

Cancel out n+3 in both numerator and denominator.

$$\frac{n+3}{n^{2}-6n+9}\times \frac{1}{2\left(n-3\right)}$$

Multiply \frac{n+3}{n^{2}-6n+9} times \frac{1}{2\left(n-3\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{n+3}{\left(n^{2}-6n+9\right)\times 2\left(n-3\right)}$$

Use the distributive property to multiply n^{2}-6n+9 by 2.

$$\frac{n+3}{\left(2n^{2}-12n+18\right)\left(n-3\right)}$$

Use the distributive property to multiply 2n^{2}-12n+18 by n-3 and combine like terms.

$$\frac{n+3}{2n^{3}-18n^{2}+54n-54}$$

Expand

$$\frac{n+3}{2\left(n-3\right)\left(n^{2}-6n+9\right)}$$

Short Solution Steps

Divide 1 by \frac{n^{2}-6n+9}{n+3} by multiplying 1 by the reciprocal of \frac{n^{2}-6n+9}{n+3}.

$$\frac{n+3}{n^{2}-6n+9}\times \frac{n+3}{2n^{2}-18}$$

Factor the expressions that are not already factored in \frac{n+3}{2n^{2}-18}.

$$\frac{n+3}{n^{2}-6n+9}\times \frac{n+3}{2\left(n-3\right)\left(n+3\right)}$$

Cancel out n+3 in both numerator and denominator.

$$\frac{n+3}{n^{2}-6n+9}\times \frac{1}{2\left(n-3\right)}$$

Multiply \frac{n+3}{n^{2}-6n+9} times \frac{1}{2\left(n-3\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{n+3}{\left(n^{2}-6n+9\right)\times 2\left(n-3\right)}$$

Use the distributive property to multiply n^{2}-6n+9 by 2.

$$\frac{n+3}{\left(2n^{2}-12n+18\right)\left(n-3\right)}$$

Use the distributive property to multiply 2n^{2}-12n+18 by n-3 and combine like terms.

$$\frac{n+3}{2n^{3}-18n^{2}+54n-54}$$