Solve x-4/x^2-25/1+frac{1{x-5}}

$$\frac { \frac { x - 4 } { x ^ { 2 } - 25 } } { 1 + \frac { 1 } { x - 5 } }$$

Evaluate

$$\frac{1}{x+5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-5}{x-5}.

$$\frac{\frac{x-4}{x^{2}-25}}{\frac{x-5}{x-5}+\frac{1}{x-5}}$$

Since \frac{x-5}{x-5} and \frac{1}{x-5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x-4}{x^{2}-25}}{\frac{x-5+1}{x-5}}$$

Combine like terms in x-5+1.

$$\frac{\frac{x-4}{x^{2}-25}}{\frac{x-4}{x-5}}$$

Divide \frac{x-4}{x^{2}-25} by \frac{x-4}{x-5} by multiplying \frac{x-4}{x^{2}-25} by the reciprocal of \frac{x-4}{x-5}.

$$\frac{\left(x-4\right)\left(x-5\right)}{\left(x^{2}-25\right)\left(x-4\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{x-5}{x^{2}-25}$$

Factor the expressions that are not already factored.

$$\frac{x-5}{\left(x-5\right)\left(x+5\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{1}{x+5}$$

Expand

$$\frac{1}{x+5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-5}{x-5}.

$$\frac{\frac{x-4}{x^{2}-25}}{\frac{x-5}{x-5}+\frac{1}{x-5}}$$

Since \frac{x-5}{x-5} and \frac{1}{x-5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x-4}{x^{2}-25}}{\frac{x-5+1}{x-5}}$$

Combine like terms in x-5+1.

$$\frac{\frac{x-4}{x^{2}-25}}{\frac{x-4}{x-5}}$$

Divide \frac{x-4}{x^{2}-25} by \frac{x-4}{x-5} by multiplying \frac{x-4}{x^{2}-25} by the reciprocal of \frac{x-4}{x-5}.

$$\frac{\left(x-4\right)\left(x-5\right)}{\left(x^{2}-25\right)\left(x-4\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{x-5}{x^{2}-25}$$

Factor the expressions that are not already factored.

$$\frac{x-5}{\left(x-5\right)\left(x+5\right)}$$

Cancel out x-5 in both numerator and denominator.

$$\frac{1}{x+5}$$