Question

subtracting rational expressions
which expression is equivalent to $\frac{x^2 - 7}{5x - 4} - \frac{2x + 9}{5x - 4}$?
$\frac{x^2 - 7 + 2x - 9}{5x - 4}$
$\frac{x^2 - 7 + 2x + 9}{5x - 4}$
$\frac{x^2 - 7 - 2x - 9}{5x - 4}$
$\frac{x^2 - 7 - 2x + 9}{5x - 4}$

Explanation:

Step1: Identify common denominator

The two rational expressions have the same denominator $5x-4$, so we can combine the numerators directly.

Step2: Distribute the subtraction to the numerator

When subtracting $\frac{2x+9}{5x-4}$, we subtract each term in its numerator:
$\frac{x^2 - 7 - (2x + 9)}{5x - 4} = \frac{x^2 - 7 - 2x - 9}{5x - 4}$

Answer:

$\boldsymbol{\frac{x^2 - 7 - 2x - 9}{5x - 4}}$ (the third option)