Solve 5x/2x^2-6x-2x/x^2-3x

$$\frac { 5 x } { 2 x ^ { 2 } - 6 x } - \frac { 2 x } { x ^ { 2 } - 3 x }$$

Evaluate

$$\frac{1}{2\left(x-3\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{5x}{2x^{2}-6x}.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{2x}{x^{2}-3x}.

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

Cancel out x in both numerator and denominator.

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

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

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

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

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

Do the multiplications in 5-2\times 2.

$$\frac{5-4}{2\left(x-3\right)}$$

Do the calculations in 5-4.

$$\frac{1}{2\left(x-3\right)}$$

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

$$\frac{1}{2x-6}$$

Factor

$$\frac{1}{2\left(x-3\right)}$$