Solve 9/x-6+x-114/x^2-36

$$\frac{ 9 }{ x-6 } + \frac{ x-114 }{ { x }^{ 2 } -36 }$$

Evaluate

$$\frac{10}{x+6}$$

Short Solution Steps

Factor x^{2}-36.

$$\frac{9}{x-6}+\frac{x-114}{\left(x-6\right)\left(x+6\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-6 and \left(x-6\right)\left(x+6\right) is \left(x-6\right)\left(x+6\right). Multiply \frac{9}{x-6} times \frac{x+6}{x+6}.

$$\frac{9\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}+\frac{x-114}{\left(x-6\right)\left(x+6\right)}$$

Since \frac{9\left(x+6\right)}{\left(x-6\right)\left(x+6\right)} and \frac{x-114}{\left(x-6\right)\left(x+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{9\left(x+6\right)+x-114}{\left(x-6\right)\left(x+6\right)}$$

Do the multiplications in 9\left(x+6\right)+x-114.

$$\frac{9x+54+x-114}{\left(x-6\right)\left(x+6\right)}$$

Combine like terms in 9x+54+x-114.

$$\frac{10x-60}{\left(x-6\right)\left(x+6\right)}$$

Factor the expressions that are not already factored in \frac{10x-60}{\left(x-6\right)\left(x+6\right)}.

$$\frac{10\left(x-6\right)}{\left(x-6\right)\left(x+6\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{10}{x+6}$$

Expand

$$\frac{10}{x+6}$$

Short Solution Steps

Factor x^{2}-36.

$$\frac{9}{x-6}+\frac{x-114}{\left(x-6\right)\left(x+6\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-6 and \left(x-6\right)\left(x+6\right) is \left(x-6\right)\left(x+6\right). Multiply \frac{9}{x-6} times \frac{x+6}{x+6}.

$$\frac{9\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}+\frac{x-114}{\left(x-6\right)\left(x+6\right)}$$

Since \frac{9\left(x+6\right)}{\left(x-6\right)\left(x+6\right)} and \frac{x-114}{\left(x-6\right)\left(x+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{9\left(x+6\right)+x-114}{\left(x-6\right)\left(x+6\right)}$$

Do the multiplications in 9\left(x+6\right)+x-114.

$$\frac{9x+54+x-114}{\left(x-6\right)\left(x+6\right)}$$

Combine like terms in 9x+54+x-114.

$$\frac{10x-60}{\left(x-6\right)\left(x+6\right)}$$

Factor the expressions that are not already factored in \frac{10x-60}{\left(x-6\right)\left(x+6\right)}.

$$\frac{10\left(x-6\right)}{\left(x-6\right)\left(x+6\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{10}{x+6}$$