Solve 5x/x^2-5/2x-6

$$\frac{ 5x }{ { x }^{ 2 } } - \frac{ 5 }{ 2x-6 }$$

Evaluate

$$\frac{5\left(x-6\right)}{2x\left(x-3\right)}$$

Short Solution Steps

Cancel out x in both numerator and denominator.

$$\frac{5}{x}-\frac{5}{2x-6}$$

Factor 2x-6.

$$\frac{5}{x}-\frac{5}{2\left(x-3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 2\left(x-3\right) is 2x\left(x-3\right). Multiply \frac{5}{x} times \frac{2\left(x-3\right)}{2\left(x-3\right)}. Multiply \frac{5}{2\left(x-3\right)} times \frac{x}{x}.

$$\frac{5\times 2\left(x-3\right)}{2x\left(x-3\right)}-\frac{5x}{2x\left(x-3\right)}$$

Since \frac{5\times 2\left(x-3\right)}{2x\left(x-3\right)} and \frac{5x}{2x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 2\left(x-3\right)-5x}{2x\left(x-3\right)}$$

Do the multiplications in 5\times 2\left(x-3\right)-5x.

$$\frac{10x-30-5x}{2x\left(x-3\right)}$$

Combine like terms in 10x-30-5x.

$$\frac{5x-30}{2x\left(x-3\right)}$$

Expand 2x\left(x-3\right).

$$\frac{5x-30}{2x^{2}-6x}$$

Factor

$$\frac{5\left(x-6\right)}{2x\left(x-3\right)}$$