Add the rational expressions.Be sure to express your answer in simplest form. $\frac { 5 } { 2 x + 3 } + \frac { 2 } { 5 x + 3 }$
A) $\frac { 29 x + 21 } { ( 2 x - 3 ) ( 5 x + 3 ) }$
B) $\frac { 28 x + 21 } { ( 2 x + 3 ) ( 5 x + 3 ) }$
C) $\frac { 29 x - 21 } { ( 2 x + 3 ) ( 5 x + 3 ) }$
D) $\frac { 29 x + 21 } { ( 2 x + 3 ) ( 5 x + 3 ) }$

Question

Quizplus · Accepted Answer

To add rational expressions, we need to find a common denominator. Here, the denominators are $2x+3$ and $5x+3$. The common denominator is $(2x+3)(5x+3)$. Thus, we can rewrite the given expressions: $$\frac{5}{2x+3}+\frac{2}{5x+3}=\frac{5(5x+3)}{(2x+3)(5x+3)}+\frac{2(2x+3)}{(2x+3)(5x+3)}=\frac{25x+15+4x+6}{(2x+3)(5x+3)}.$$ Combining like terms gives: $$\frac{29x+21}{(2x+3)(5x+3)}.$$ Therefore, the best choice is D.

Add the Rational Expressions 52x+3+25x+3\frac { 5 } { 2 x + 3 } + \frac { 2 } { 5 x + 3 }2x+35​+5x+32​

Add the Rational Expressions $\frac { 5 } { 2 x + 3 } + \frac { 2 } { 5 x + 3 }$