Solve =2x/x-3+x/x^2-7x+12

$$= \frac { 2 x } { x - 3 } + \frac { x } { x ^ { 2 } - 7 x + 12 }$$

Evaluate

$$\frac{x\left(2x-7\right)}{\left(x-4\right)\left(x-3\right)}$$

Short Solution Steps

Factor x^{2}-7x+12.

$$\frac{2x}{x-3}+\frac{x}{\left(x-4\right)\left(x-3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-3 and \left(x-4\right)\left(x-3\right) is \left(x-4\right)\left(x-3\right). Multiply \frac{2x}{x-3} times \frac{x-4}{x-4}.

$$\frac{2x\left(x-4\right)}{\left(x-4\right)\left(x-3\right)}+\frac{x}{\left(x-4\right)\left(x-3\right)}$$

Since \frac{2x\left(x-4\right)}{\left(x-4\right)\left(x-3\right)} and \frac{x}{\left(x-4\right)\left(x-3\right)} have the same denominator, add them by adding their numerators.

$$\frac{2x\left(x-4\right)+x}{\left(x-4\right)\left(x-3\right)}$$

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

$$\frac{2x^{2}-8x+x}{\left(x-4\right)\left(x-3\right)}$$

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

$$\frac{2x^{2}-7x}{\left(x-4\right)\left(x-3\right)}$$

Expand \left(x-4\right)\left(x-3\right).

$$\frac{2x^{2}-7x}{x^{2}-7x+12}$$

Factor

$$\frac{x\left(2x-7\right)}{\left(x-4\right)\left(x-3\right)}$$