Question

simplify the rational expression
\\(\dfrac{\dfrac{1}{x + 6} - \dfrac{1}{9}}{x - 3}\\)

Explanation:

Step1: Simplify numerator

$\frac{1}{x+6} - \frac{1}{9} = \frac{9 - (x+6)}{9(x+6)} = \frac{3 - x}{9(x+6)}$

Step2: Divide by denominator

$\frac{\frac{3 - x}{9(x+6)}}{x - 3} = \frac{3 - x}{9(x+6)} \cdot \frac{1}{x - 3} = \frac{-(x - 3)}{9(x+6)(x - 3)}$

Step3: Cancel common terms

$\frac{-1}{9(x+6)}$

Answer:

$\frac{-1}{9(x+6)}$