Solve 2x/x-3-3x/x-5

$$\frac { 2 x } { x - 3 } - \frac { 3 x } { x - 5 }$$

Evaluate

$$-\frac{x\left(x+1\right)}{\left(x-5\right)\left(x-3\right)}$$

Short Solution Steps

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

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

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

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

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

$$\frac{2x^{2}-10x-3x^{2}+9x}{\left(x-5\right)\left(x-3\right)}$$

Combine like terms in 2x^{2}-10x-3x^{2}+9x.

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

Expand \left(x-5\right)\left(x-3\right).

$$\frac{-x^{2}-x}{x^{2}-8x+15}$$

Factor

$$-\frac{x\left(x+1\right)}{\left(x-5\right)\left(x-3\right)}$$