Solve 4x/6x-24-7/4x-16

$$\frac { 4 x } { 6 x - 24 } - \frac { 7 } { 4 x - 16 }$$

Evaluate

$$\frac{8x-21}{12\left(x-4\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4x}{6x-24}.

$$\frac{4x}{6\left(x-4\right)}-\frac{7}{4x-16}$$

Cancel out 2 in both numerator and denominator.

$$\frac{2x}{3\left(x-4\right)}-\frac{7}{4x-16}$$

Factor 4x-16.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(x-4\right) and 4\left(x-4\right) is 12\left(x-4\right). Multiply \frac{2x}{3\left(x-4\right)} times \frac{4}{4}. Multiply \frac{7}{4\left(x-4\right)} times \frac{3}{3}.

$$\frac{4\times 2x}{12\left(x-4\right)}-\frac{7\times 3}{12\left(x-4\right)}$$

Since \frac{4\times 2x}{12\left(x-4\right)} and \frac{7\times 3}{12\left(x-4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\times 2x-7\times 3}{12\left(x-4\right)}$$

Do the multiplications in 4\times 2x-7\times 3.

$$\frac{8x-21}{12\left(x-4\right)}$$

Expand 12\left(x-4\right).

$$\frac{8x-21}{12x-48}$$

Factor

$$\frac{8x-21}{12\left(x-4\right)}$$