Divide. $\frac { 24 w ^ { 4 } r ^ { 4 } + 32 w ^ { 3 } r ^ { 3 } - 40 w ^ { 2 } r ^ { 2 } } { 8 w ^ { 3 } r ^ { 3 } }$
A) $3 w r + 5 - \frac { 4 } { w r }$
B) $3 w r + 4 w - \frac { 5 } { w r ^ { 3 } }$
C) $3 w r ^ { 2 } + 4 - \frac { 5 } { w r }$
D) $3 w r + 5 + \frac { 4 } { w r }$
E) $3 w r + 4 - \frac { 5 } { w r }$

Question

Quizplus · Accepted Answer

We can simplify the numerator by factoring out the greatest common factor of $8w^2r^2$:

$$\frac{24w^4r^4+32w^3r^3-40w^2r^2}{8w^3r^3}=\frac{8w^2r^2(3w^2r^2+4wr-5)}{8w^3r^3}$$

Now we can cancel out the $8$ and one of the $w$'s and one of the $r$'s, leaving us with:

$$\frac{8w^2r^2(3w^2r^2+4wr-5)}{8w^3r^3}=\frac{3w^2r^2+4wr-5}{w^2r^2}$$

This is equal to:

$$\frac{3}{wr}+\frac{4}{w}-\frac{5}{w^2r^2}$$

And finally, rearranging the terms gives:

$$\frac{3}{w}r+4-\frac{5}{wr^2}$$

Therefore, the answer is $\boxed{	extbf{(E)}}$.

Divide 24w4r4+32w3r3−40w2r28w3r3\frac { 24 w ^ { 4 } r ^ { 4 } + 32 w ^ { 3 } r ^ { 3 } - 40 w ^ { 2 } r ^ { 2 } } { 8 w ^ { 3 } r ^ { 3 } }8w3r324w4r4+32w3r3−40w2r2​

Divide $\frac { 24 w ^ { 4 } r ^ { 4 } + 32 w ^ { 3 } r ^ { 3 } - 40 w ^ { 2 } r ^ { 2 } } { 8 w ^ { 3 } r ^ { 3 } }$