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

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

Evaluate

$$\frac{8-5x^{2}}{x\left(x+2\right)}$$

Short Solution Steps

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

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

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

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

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

$$\frac{4x+8-5x^{2}-4x}{x\left(x+2\right)}$$

Combine like terms in 4x+8-5x^{2}-4x.

$$\frac{8-5x^{2}}{x\left(x+2\right)}$$

Expand x\left(x+2\right).

$$\frac{8-5x^{2}}{x^{2}+2x}$$

Expand

$$\frac{8-5x^{2}}{x\left(x+2\right)}$$

Short Solution Steps

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

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

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

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

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

$$\frac{4x+8-5x^{2}-4x}{x\left(x+2\right)}$$

Combine like terms in 4x+8-5x^{2}-4x.

$$\frac{8-5x^{2}}{x\left(x+2\right)}$$

Expand x\left(x+2\right).

$$\frac{8-5x^{2}}{x^{2}+2x}$$