Answer:
x = 4
Step-by-step explanation:
Given
[tex]\frac{3}{x+4}[/tex] - [tex]\frac{1}{x+3}[/tex] = [tex]\frac{x+9}{x^2+7x+12}[/tex] ← factor the quadratic
[tex]\frac{3}{x+4}[/tex] - [tex]\frac{1}{x+3}[/tex] = [tex]\frac{x+9}{(x+3)(x+4)}[/tex]
Multiply through by (x + 3)(x + 4) to clear the fractions
3(x+3) - (x + 4) = x + 9 ← distribute and simplify left side
3x + 9 - x - 4 = x + 9
2x + 5 = x + 9 ( subtract x from both sides )
x + 5 = 9 ( subtract 5 from both sides )
x = 4
