Solve 4x/x^2-36+24/x-6

$$\frac { 4 x } { x ^ { 2 } - 36 } + \frac { 24 } { x - 6 }$$

Evaluate

$$\frac{4\left(7x+36\right)}{x^{2}-36}$$

Short Solution Steps

Factor x^{2}-36.

$$\frac{4x}{\left(x-6\right)\left(x+6\right)}+\frac{24}{x-6}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-6\right)\left(x+6\right) and x-6 is \left(x-6\right)\left(x+6\right). Multiply \frac{24}{x-6} times \frac{x+6}{x+6}.

$$\frac{4x}{\left(x-6\right)\left(x+6\right)}+\frac{24\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}$$

Since \frac{4x}{\left(x-6\right)\left(x+6\right)} and \frac{24\left(x+6\right)}{\left(x-6\right)\left(x+6\right)} have the same denominator, add them by adding their numerators.

$$\frac{4x+24\left(x+6\right)}{\left(x-6\right)\left(x+6\right)}$$

Do the multiplications in 4x+24\left(x+6\right).

$$\frac{4x+24x+144}{\left(x-6\right)\left(x+6\right)}$$

Combine like terms in 4x+24x+144.

$$\frac{28x+144}{\left(x-6\right)\left(x+6\right)}$$

Expand \left(x-6\right)\left(x+6\right).

$$\frac{28x+144}{x^{2}-36}$$

Factor

$$\frac{4\left(7x+36\right)}{x^{2}-36}$$