Solve 2x/x-7-x/x-3

$$\frac { 2 x } { x - 7 } - \frac { x } { x - 3 }$$

Evaluate

$$\frac{x\left(x+1\right)}{\left(x-7\right)\left(x-3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-7 and x-3 is \left(x-7\right)\left(x-3\right). Multiply \frac{2x}{x-7} times \frac{x-3}{x-3}. Multiply \frac{x}{x-3} times \frac{x-7}{x-7}.

$$\frac{2x\left(x-3\right)}{\left(x-7\right)\left(x-3\right)}-\frac{x\left(x-7\right)}{\left(x-7\right)\left(x-3\right)}$$

Since \frac{2x\left(x-3\right)}{\left(x-7\right)\left(x-3\right)} and \frac{x\left(x-7\right)}{\left(x-7\right)\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x\left(x-3\right)-x\left(x-7\right)}{\left(x-7\right)\left(x-3\right)}$$

Do the multiplications in 2x\left(x-3\right)-x\left(x-7\right).

$$\frac{2x^{2}-6x-x^{2}+7x}{\left(x-7\right)\left(x-3\right)}$$

Combine like terms in 2x^{2}-6x-x^{2}+7x.

$$\frac{x^{2}+x}{\left(x-7\right)\left(x-3\right)}$$

Expand \left(x-7\right)\left(x-3\right).

$$\frac{x^{2}+x}{x^{2}-10x+21}$$

Factor

$$\frac{x\left(x+1\right)}{\left(x-7\right)\left(x-3\right)}$$