Perform the indicated operation. Simplify, if possible.
-$\frac{3 x+9}{x+2}+\frac{x+3}{x+4}-\frac{2 x+10}{(x+2)(x+4)}$
A) 4
B) $\frac{3}{(x+2)}$
C) $\frac{4}{(x+2)(x+4)}$
D) $\frac{1}{(x+2)(x+4)}$

Question

Quizplus · Accepted Answer

The least common denominator is (x+2)(x+4). Multiplying the first fraction by (x+4)/(x+4), the second fraction by (x+2)/(x+2), and the third fraction by 1/(1), we get:$\frac{(3x+9)(x+4)}{(x+2)(x+4)}+\frac{(x+3)(x+2)}{(x+2)(x+4)}-\frac{(2x+10)}{(x+2)(x+4)}$Combining like terms, we get:$\frac{(3x^2+15x+9x+36)+(x^2+5x+6x+6)-(2x+10)}{(x+2)(x+4)}$Simplifying, we get:$\frac{4x^2+25x+42}{(x+2)(x+4)}$Factoring the numerator, we get:$\frac{(4x+21)(x+2)}{(x+2)(x+4)}$Canceling the common factor of (x+2), we get:$\frac{4x+21}{x+4}$

Perform the Indicated Operation 3x+9x+2+x+3x+4−2x+10(x+2)(x+4)\frac{3 x+9}{x+2}+\frac{x+3}{x+4}-\frac{2 x+10}{(x+2)(x+4)}x+23x+9​+x+4x+3​−(x+2)(x+4)2x+10​ A) 4 B) 3(x+2)\frac{3}{(x+2)}(x+2)3​ C) 4(x+2)(x+4)\frac{4}{(x+2)(x+4)}(x+2)(x+4)4​

Perform the Indicated Operation $\frac{3 x+9}{x+2}+\frac{x+3}{x+4}-\frac{2 x+10}{(x+2)(x+4)}$ A) 4
B) $\frac{3}{(x+2)}$ C) $\frac{4}{(x+2)(x+4)}$