Solve 5/2x-3-3x-8/4x-6

$$\frac{ 5 }{ 2x-3 } - \frac{ 3x-8 }{ 4x-6 }$$

Evaluate

$$\frac{3\left(6-x\right)}{2\left(2x-3\right)}$$

Short Solution Steps

Factor 4x-6.

$$\frac{5}{2x-3}-\frac{3x-8}{2\left(2x-3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-3 and 2\left(2x-3\right) is 2\left(2x-3\right). Multiply \frac{5}{2x-3} times \frac{2}{2}.

$$\frac{5\times 2}{2\left(2x-3\right)}-\frac{3x-8}{2\left(2x-3\right)}$$

Since \frac{5\times 2}{2\left(2x-3\right)} and \frac{3x-8}{2\left(2x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 2-\left(3x-8\right)}{2\left(2x-3\right)}$$

Do the multiplications in 5\times 2-\left(3x-8\right).

$$\frac{10-3x+8}{2\left(2x-3\right)}$$

Combine like terms in 10-3x+8.

$$\frac{18-3x}{2\left(2x-3\right)}$$

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

$$\frac{18-3x}{4x-6}$$

Expand

$$-\frac{3\left(x-6\right)}{2\left(2x-3\right)}$$

Short Solution Steps

Factor 4x-6.

$$\frac{5}{2x-3}-\frac{3x-8}{2\left(2x-3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-3 and 2\left(2x-3\right) is 2\left(2x-3\right). Multiply \frac{5}{2x-3} times \frac{2}{2}.

$$\frac{5\times 2}{2\left(2x-3\right)}-\frac{3x-8}{2\left(2x-3\right)}$$

Since \frac{5\times 2}{2\left(2x-3\right)} and \frac{3x-8}{2\left(2x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 2-\left(3x-8\right)}{2\left(2x-3\right)}$$

Do the multiplications in 5\times 2-\left(3x-8\right).

$$\frac{10-3x+8}{2\left(2x-3\right)}$$

Combine like terms in 10-3x+8.

$$\frac{18-3x}{2\left(2x-3\right)}$$

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

$$\frac{18-3x}{4x-6}$$