Solve x^2-9/(x-6)^2-27/(6-x)^2

$$\frac { x ^ { 2 } - 9 } { ( x - 6 ) ^ { 2 } } - \frac { 27 } { ( 6 - x ) ^ { 2 } }$$

Evaluate

$$\frac{x+6}{x-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Expand \left(6-x\right)^{2}.

$$\frac{x^{2}-9}{\left(x-6\right)^{2}}-\frac{27}{\left(x-6\right)^{2}}$$

Since \frac{x^{2}-9}{\left(x-6\right)^{2}} and \frac{27}{\left(x-6\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-9-27}{\left(x-6\right)^{2}}$$

Combine like terms in x^{2}-9-27.

$$\frac{x^{2}-36}{\left(x-6\right)^{2}}$$

Factor the expressions that are not already factored in \frac{x^{2}-36}{\left(x-6\right)^{2}}.

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

Cancel out x-6 in both numerator and denominator.

$$\frac{x+6}{x-6}$$

Expand

$$\frac{x+6}{x-6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Expand \left(6-x\right)^{2}.

$$\frac{x^{2}-9}{\left(x-6\right)^{2}}-\frac{27}{\left(x-6\right)^{2}}$$

Since \frac{x^{2}-9}{\left(x-6\right)^{2}} and \frac{27}{\left(x-6\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-9-27}{\left(x-6\right)^{2}}$$

Combine like terms in x^{2}-9-27.

$$\frac{x^{2}-36}{\left(x-6\right)^{2}}$$

Factor the expressions that are not already factored in \frac{x^{2}-36}{\left(x-6\right)^{2}}.

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

Cancel out x-6 in both numerator and denominator.

$$\frac{x+6}{x-6}$$