Multiply and simplify. $\frac { 12 u ^ { 6 } v } { 7 u + v } \cdot \frac { u + v } { 18 u ^ { 5 } }$
A) $\frac { 6 u v } { 7 } , u \neq 0$
B) $\frac { u + v } { 7 } , u \neq 0$
C) $\frac { 2 u v ( u + v ) } { 3 ( 7 u + v ) } , u \neq 0$
D) $\frac { 2 ( u + v ) } { 3 ( 7 u + v ) } , u \neq 0$
E) $\frac { 6 } { 7 u + v } , u \neq 0$

Question

Quizplus · Accepted Answer

We start by simplifying each fraction individually.

$$\frac { 12 u ^ { 6 } v } { 7 u + v } = \frac{4u^5 \cdot 3u v}{7u + v}$$
$$\frac { u + v } { 18 u ^ { 5 } } = \frac{1}{18u^4}(u+v)$$

Now, we can multiply the two fractions.

$$\frac { 12 u ^ { 6 } v } { 7 u + v } \cdot \frac { u + v } { 18 u ^ { 5 } } = \frac{4u^5 \cdot 3u v}{7u + v}\cdot \frac{1}{18u^4}(u+v)$$
$$=\frac{12u^6v}{7u+v} \cdot \frac{1}{18u^4}(u+v) = \boxed{\textbf{(C) } \frac{2 u v ( u + v )}{3 ( 7 u + v )}}, \text{ for }u\neq0$$

Multiply and Simplify 12u6v7u+v⋅u+v18u5\frac { 12 u ^ { 6 } v } { 7 u + v } \cdot \frac { u + v } { 18 u ^ { 5 } }7u+v12u6v​⋅18u5u+v​

Multiply and Simplify $\frac { 12 u ^ { 6 } v } { 7 u + v } \cdot \frac { u + v } { 18 u ^ { 5 } }$