Add or subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 3 } { 2 m } + \frac { 4 } { 3 n } - 3$
A) $\frac { 9 n + 8 m - m n } { 6 m n }$
B) $\frac { 6 n + 12 m - 6 m - 9 n } { 2 m + 3 n }$
C) $\frac { 9 n + 8 m } { 6 m n }$
D) $\frac { 9 n + 8 m } { 2 m + 3 n } - 3$
E) $\frac { 9 n + 8 m - 18 m n } { 6 m n }$

Question

Quizplus · Accepted Answer

To add or subtract rational expressions, you need a common denominator. The common denominator for $\frac{3}{2m}$ and $\frac{4}{3n}$ is $6mn$. Convert each fraction to have this common denominator: $\frac{3}{2m} = \frac{9n}{6mn}$, $\frac{4}{3n} = \frac{8m}{6mn}$. The term $3$ can be expressed as $\frac{18mn}{6mn}$. Adding these gives $\frac{9n + 8m - 18mn}{6mn}$, which matches choice E.

Add or Subtract the Rational Expressions 32m+43n−3\frac { 3 } { 2 m } + \frac { 4 } { 3 n } - 32m3​+3n4​−3

Add or Subtract the Rational Expressions $\frac { 3 } { 2 m } + \frac { 4 } { 3 n } - 3$