Question

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

Explanation:

Step1: Combine fractions (common denominator)

Since both fractions have the same denominator \(a-5\), add the numerators directly:
$$\frac{a^2 - 7a + 3a - 5}{a-5}$$

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 common factor \(a-5\) (where \(a
eq 5\)):
$$a+1$$

Answer:

\(a + 1\)