Solve 15x/15x-9-9/15x-9

$$\frac { 15 x } { 15 x - 9 } - \frac { 9 } { 15 x - 9 }$$

Evaluate

$$1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{15x}{15x-9}.

$$\frac{15x}{3\left(5x-3\right)}-\frac{9}{15x-9}$$

Cancel out 3 in both numerator and denominator.

$$\frac{5x}{5x-3}-\frac{9}{15x-9}$$

Factor 15x-9.

$$\frac{5x}{5x-3}-\frac{9}{3\left(5x-3\right)}$$

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

$$\frac{3\times 5x}{3\left(5x-3\right)}-\frac{9}{3\left(5x-3\right)}$$

Since \frac{3\times 5x}{3\left(5x-3\right)} and \frac{9}{3\left(5x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 5x-9}{3\left(5x-3\right)}$$

Do the multiplications in 3\times 5x-9.

$$\frac{15x-9}{3\left(5x-3\right)}$$

Factor the expressions that are not already factored in \frac{15x-9}{3\left(5x-3\right)}.

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

Cancel out 3\left(5x-3\right) in both numerator and denominator.

$$1$$

Factor

$$1$$