Solve 4/x+5+2x/x^2-25

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

Evaluate

$$\frac{2\left(3x-10\right)}{x^{2}-25}$$

Short Solution Steps

Factor x^{2}-25.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+5 and \left(x-5\right)\left(x+5\right) is \left(x-5\right)\left(x+5\right). Multiply \frac{4}{x+5} times \frac{x-5}{x-5}.

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

Since \frac{4\left(x-5\right)}{\left(x-5\right)\left(x+5\right)} and \frac{2x}{\left(x-5\right)\left(x+5\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4\left(x-5\right)+2x.

$$\frac{4x-20+2x}{\left(x-5\right)\left(x+5\right)}$$

Combine like terms in 4x-20+2x.

$$\frac{6x-20}{\left(x-5\right)\left(x+5\right)}$$

Expand \left(x-5\right)\left(x+5\right).

$$\frac{6x-20}{x^{2}-25}$$

Factor

$$\frac{2\left(3x-10\right)}{x^{2}-25}$$