Question

add.
\\(\frac{a^2 - 7a}{a - 5} + \frac{3a - 5}{a - 5}\\)
simplify your answer as much as possible.

Explanation:

Step1: Combine the fractions

Since the denominators are equal, add the numerators over the common denominator:
$\frac{a^2 - 7a + 3a - 5}{a - 5}$

Step2: Combine like terms in numerator

Combine the linear terms in the numerator:
$\frac{a^2 - 4a - 5}{a - 5}$

Step3: Factor the numerator

Factor the quadratic expression in the numerator:
$\frac{(a - 5)(a + 1)}{a - 5}$

Step4: Cancel common factors

Cancel the non-zero common factor $a - 5$:
$a + 1$ (where $a
eq 5$)

Answer:

$a + 1$