Question

1. simplify.

\\(\frac{3a}{a^2 - 9a + 18} - \frac{2}{a - 6}\\)
options:
\\(\frac{-3a + 44}{(a - 6)(a + 8)}\\)
\\(\frac{a + 6}{a^2 - 9a + 18}\\)
\\(\frac{a^2 + 18a + 44}{2a^2 + 44}\\)
\\(\frac{2a^2 - 28}{(a - 6)(a + 8)}\\)

Explanation:

Step1: Factor denominator

$a^2 - 9a + 18 = (a - 3)(a - 6)$

Step2: Find common denominator

Common denominator: $(a - 3)(a - 6)$

Step3: Rewrite second fraction

$\frac{2}{a - 6} = \frac{2(a - 3)}{(a - 3)(a - 6)}$

Step4: Subtract fractions

$\frac{3a - 2(a - 3)}{(a - 3)(a - 6)} = \frac{3a - 2a + 6}{(a - 3)(a - 6)}$

Step5: Simplify numerator

$\frac{a + 6}{(a - 3)(a - 6)} = \frac{a + 6}{a^2 - 9a + 18}$

Answer:

$\frac{a + 6}{a^2 - 9a + 18}$