$\frac{3 \mathrm{x}+12}{\mathrm{x}^{2}-3 \mathrm{x}-18}-\frac{\mathrm{x}+6}{\mathrm{x}^{2}-3 \mathrm{x}-18}$

A) $2 x+6$

B) $\frac{2}{x-6}$

C) $\frac{2 x+18}{x^{2}-3 x-18}$

D) $\frac{1}{x-3}$

Question

$\frac{3 \mathrm{x}+12}{\mathrm{x}^{2}-3 \mathrm{x}-18}-\frac{\mathrm{x}+6}{\mathrm{x}^{2}-3 \mathrm{x}-18}$

A) $2 x+6$

B) $\frac{2}{x-6}$

C) $\frac{2 x+18}{x^{2}-3 x-18}$

D) $\frac{1}{x-3}$

Quizplus · Accepted Answer

The expression can be simplified by combining the fractions since they have the same denominator. Subtract the numerators: $(3x + 12) - (x + 6) = 2x + 6$. The expression becomes $\frac{2x + 6}{x^2 - 3x - 18}$. Factor the numerator as $2(x + 3)$ and the denominator as $(x - 6)(x + 3)$. Cancel the common factor $(x + 3)$, resulting in $\frac{2}{x - 6}$.

3x+12x2−3x−18−x+6x2−3x−18\frac{3 \mathrm{x}+12}{\mathrm{x}^{2}-3 \mathrm{x}-18}-\frac{\mathrm{x}+6}{\mathrm{x}^{2}-3 \mathrm{x}-18}x2−3x−183x+12​−x2−3x−18x+6​ A) 2x+62 x+62x+6 B) 2x−6\frac{2}{x-6}x−62​ C) 2x+18x2−3x−18\frac{2 x+18}{x^{2}-3 x-18}x2−3x−182x+18​

$\frac{3 \mathrm{x}+12}{\mathrm{x}^{2}-3 \mathrm{x}-18}-\frac{\mathrm{x}+6}{\mathrm{x}^{2}-3 \mathrm{x}-18}$ A) $2 x+6$ B) $\frac{2}{x-6}$ C) $\frac{2 x+18}{x^{2}-3 x-18}$