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

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

Evaluate

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

Short Solution Steps

Factor x^{2}-25. Factor x^{2}+5x.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and x\left(x+5\right) is x\left(x-5\right)\left(x+5\right). Multiply \frac{4x}{\left(x-5\right)\left(x+5\right)} times \frac{x}{x}. Multiply \frac{2}{x\left(x+5\right)} times \frac{x-5}{x-5}.

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

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

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

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

$$\frac{4x^{2}-2x+10}{x\left(x-5\right)\left(x+5\right)}$$

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

$$\frac{4x^{2}-2x+10}{x^{3}-25x}$$

Factor

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