Question

find the sum
\frac{x - 5}{x + 5} + \frac{3x - 21}{x + 5}

Explanation:

Step1: Combine numerators (common denominator)

Since the denominators are identical ($x+5$), we add the numerators directly:
$\frac{(x-5) + (3x-21)}{x+5}$

Step2: Simplify the numerator

Combine like terms in the numerator:
$\frac{x + 3x -5 -21}{x+5} = \frac{4x -26}{x+5}$

Step3: Factor numerator (optional simplification)

Factor out a 2 from the numerator:
$\frac{2(2x -13)}{x+5}$

Answer:

$\frac{4x-26}{x+5}$ or $\frac{2(2x-13)}{x+5}$