Solve x-3/4x-8-5/x-2

$$\frac { x - 3 } { 4 x - 8 } - \frac { 5 } { x - 2 }$$

Evaluate

$$\frac{x-23}{4\left(x-2\right)}$$

Short Solution Steps

Factor 4x-8.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(x-2\right) and x-2 is 4\left(x-2\right). Multiply \frac{5}{x-2} times \frac{4}{4}.

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

Since \frac{x-3}{4\left(x-2\right)} and \frac{5\times 4}{4\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x-3-5\times 4.

$$\frac{x-3-20}{4\left(x-2\right)}$$

Combine like terms in x-3-20.

$$\frac{x-23}{4\left(x-2\right)}$$

Expand 4\left(x-2\right).

$$\frac{x-23}{4x-8}$$

Expand

$$\frac{x-23}{4\left(x-2\right)}$$

Short Solution Steps

Factor 4x-8.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(x-2\right) and x-2 is 4\left(x-2\right). Multiply \frac{5}{x-2} times \frac{4}{4}.

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

Since \frac{x-3}{4\left(x-2\right)} and \frac{5\times 4}{4\left(x-2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x-3-5\times 4.

$$\frac{x-3-20}{4\left(x-2\right)}$$

Combine like terms in x-3-20.

$$\frac{x-23}{4\left(x-2\right)}$$

Expand 4\left(x-2\right).

$$\frac{x-23}{4x-8}$$