Solve x-11/x^2-144/1+frac{1{x-12}}-1/x-12

$$\frac { \frac { x - 11 } { x ^ { 2 } - 144 } } { 1 + \frac { 1 } { x - 12 } } - \frac { 1 } { x - 12 }$$

Evaluate

$$-\frac{24}{x^{2}-144}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-12}{x-12}.

$$\frac{\frac{x-11}{x^{2}-144}}{\frac{x-12}{x-12}+\frac{1}{x-12}}-\frac{1}{x-12}$$

Since \frac{x-12}{x-12} and \frac{1}{x-12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x-11}{x^{2}-144}}{\frac{x-12+1}{x-12}}-\frac{1}{x-12}$$

Combine like terms in x-12+1.

$$\frac{\frac{x-11}{x^{2}-144}}{\frac{x-11}{x-12}}-\frac{1}{x-12}$$

Divide \frac{x-11}{x^{2}-144} by \frac{x-11}{x-12} by multiplying \frac{x-11}{x^{2}-144} by the reciprocal of \frac{x-11}{x-12}.

$$\frac{\left(x-11\right)\left(x-12\right)}{\left(x^{2}-144\right)\left(x-11\right)}-\frac{1}{x-12}$$

Cancel out x-11 in both numerator and denominator.

$$\frac{x-12}{x^{2}-144}-\frac{1}{x-12}$$

Factor the expressions that are not already factored in \frac{x-12}{x^{2}-144}.

$$\frac{x-12}{\left(x-12\right)\left(x+12\right)}-\frac{1}{x-12}$$

Cancel out x-12 in both numerator and denominator.

$$\frac{1}{x+12}-\frac{1}{x-12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+12 and x-12 is \left(x-12\right)\left(x+12\right). Multiply \frac{1}{x+12} times \frac{x-12}{x-12}. Multiply \frac{1}{x-12} times \frac{x+12}{x+12}.

$$\frac{x-12}{\left(x-12\right)\left(x+12\right)}-\frac{x+12}{\left(x-12\right)\left(x+12\right)}$$

Since \frac{x-12}{\left(x-12\right)\left(x+12\right)} and \frac{x+12}{\left(x-12\right)\left(x+12\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-12-\left(x+12\right)}{\left(x-12\right)\left(x+12\right)}$$

Do the multiplications in x-12-\left(x+12\right).

$$\frac{x-12-x-12}{\left(x-12\right)\left(x+12\right)}$$

Combine like terms in x-12-x-12.

$$\frac{-24}{\left(x-12\right)\left(x+12\right)}$$

Expand \left(x-12\right)\left(x+12\right).

$$\frac{-24}{x^{2}-144}$$

Expand

$$-\frac{24}{x^{2}-144}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-12}{x-12}.

$$\frac{\frac{x-11}{x^{2}-144}}{\frac{x-12}{x-12}+\frac{1}{x-12}}-\frac{1}{x-12}$$

Since \frac{x-12}{x-12} and \frac{1}{x-12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{x-11}{x^{2}-144}}{\frac{x-12+1}{x-12}}-\frac{1}{x-12}$$

Combine like terms in x-12+1.

$$\frac{\frac{x-11}{x^{2}-144}}{\frac{x-11}{x-12}}-\frac{1}{x-12}$$

Divide \frac{x-11}{x^{2}-144} by \frac{x-11}{x-12} by multiplying \frac{x-11}{x^{2}-144} by the reciprocal of \frac{x-11}{x-12}.

$$\frac{\left(x-11\right)\left(x-12\right)}{\left(x^{2}-144\right)\left(x-11\right)}-\frac{1}{x-12}$$

Cancel out x-11 in both numerator and denominator.

$$\frac{x-12}{x^{2}-144}-\frac{1}{x-12}$$

Factor the expressions that are not already factored in \frac{x-12}{x^{2}-144}.

$$\frac{x-12}{\left(x-12\right)\left(x+12\right)}-\frac{1}{x-12}$$

Cancel out x-12 in both numerator and denominator.

$$\frac{1}{x+12}-\frac{1}{x-12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+12 and x-12 is \left(x-12\right)\left(x+12\right). Multiply \frac{1}{x+12} times \frac{x-12}{x-12}. Multiply \frac{1}{x-12} times \frac{x+12}{x+12}.

$$\frac{x-12}{\left(x-12\right)\left(x+12\right)}-\frac{x+12}{\left(x-12\right)\left(x+12\right)}$$

Since \frac{x-12}{\left(x-12\right)\left(x+12\right)} and \frac{x+12}{\left(x-12\right)\left(x+12\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-12-\left(x+12\right)}{\left(x-12\right)\left(x+12\right)}$$

Do the multiplications in x-12-\left(x+12\right).

$$\frac{x-12-x-12}{\left(x-12\right)\left(x+12\right)}$$

Combine like terms in x-12-x-12.

$$\frac{-24}{\left(x-12\right)\left(x+12\right)}$$

Expand \left(x-12\right)\left(x+12\right).

$$\frac{-24}{x^{2}-144}$$