Subtract the rational expressions. Be sure to express your answer in simplest form. $\frac { 5 } { 8 x ^ { 2 } y } - \frac { 2 x } { 4 y ^ { 2 } }$
A) $\frac { 5 y - 4 x } { 8 x ^ { 2 } y ^ { 2 } }$
B) $\frac { 5 y - 4 x ^ { 3 } } { 8 x ^ { 2 } y }$
C) $\frac { 5 - 4 x ^ { 3 } } { 8 x ^ { 2 } y ^ { 2 } }$
D) $\frac { 5 y - 4 x ^ { 3 } } { 8 x ^ { 2 } y ^ { 2 } }$

Question

Quizplus · Accepted Answer

To subtract rational expressions, we first need to find a common denominator. In this case, the denominators are $8x^2y$ and $4y^2$. Notice that $8x^2y$ can be factored as $4\cdot2x^2y$, so we can rewrite the first fraction as $\frac{5}{4\cdot2x^2y}$. Then, we can rewrite the second fraction with a denominator of $8x^2y$ by multiplying the top and bottom by 2: $$\frac{2x\cdot2}{4y^2\cdot2}= \frac{4x}{8y^2}= \frac{x}{2y^2}$$ Now we can rewrite the original expression as: $$\frac { 5 } { 8 x ^ { 2 } y } - \frac { 2 x } { 4 y ^ { 2 } } = \frac{5}{4\cdot2x^2y}-\frac{x}{2y^2}$$ Finding a common denominator, we get: $$\frac{5}{4\cdot2x^2y}-\frac{x}{2y^2} = \frac{5}{8x^2y^2}-\frac{4x^3}{8x^2y^2}=\frac{5-4x^3}{8x^2y^2}$$ Therefore, the answer is D.

Subtract the Rational Expressions 58x2y−2x4y2\frac { 5 } { 8 x ^ { 2 } y } - \frac { 2 x } { 4 y ^ { 2 } }8x2y5​−4y22x​

Subtract the Rational Expressions $\frac { 5 } { 8 x ^ { 2 } y } - \frac { 2 x } { 4 y ^ { 2 } }$