Question

Add$\frac{8x-15}{2x-5}+\frac{2x}{2x-5}$.

Short answer

The required expression is$3$.

Step-by-step solution

Given information

The given expression is $\frac{8x-15}{2x-5}+\frac{2x}{5-2x}$

Simplifying the expression

The denominators of both the terms are opposite, so Multiply the second expression by $\frac{-1}{-1}$:

$\frac{8x-15}{2x-5}+\frac{(-1)2x}{(-1)(5-2x)}$

Simplify the second expression:

$\frac{8x-15}{2x-5}+\frac{-2x}{2x-5}$

Make the denominator same:

$\frac{8x-15-2x}{2x-5}$

Combine like terms:

$\frac{6x-15}{2x-5}$

Factor the numerator:

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

Cancel the like terms:

$3$