Simplify.
-$\frac{\frac{4}{3 x^{3}}-\frac{3}{6 x}}{\frac{3}{2 x}+\frac{3}{3 x^{3}}}$
A) $\frac{8+3 x^{2}}{9 x^{2}+2}$
B) $\frac{4-3 x^{2}}{3 x^{2}-6}$
C) $\frac{8-9 x^{2}}{9 x^{2}+6}$
D) $\frac{8-3 x^{2}}{9 x^{2}+6}$

Question

Quizplus · Accepted Answer

First, simplify the fractions within the numerator and the denominator by finding a common denominator for each. For the numerator, the common denominator is $6x^3$, and for the denominator, it's $6x^3$. Simplifying within those constraints and then simplifying the resulting fraction leads to the correct answer, which matches option D: $\frac{8-3 x^{2}}{9 x^{2}+6}$.

Simplify - 43x3−36x32x+33x3\frac{\frac{4}{3 x^{3}}-\frac{3}{6 x}}{\frac{3}{2 x}+\frac{3}{3 x^{3}}}2x3​+3x33​3x34​−6x3​​ A) 8+3x29x2+2\frac{8+3 x^{2}}{9 x^{2}+2}9x2+28+3x2​ B) 4−3x23x2−6\frac{4-3 x^{2}}{3 x^{2}-6}3x2−64−3x2​

Simplify
- $\frac{\frac{4}{3 x^{3}}-\frac{3}{6 x}}{\frac{3}{2 x}+\frac{3}{3 x^{3}}}$ A) $\frac{8+3 x^{2}}{9 x^{2}+2}$ B) $\frac{4-3 x^{2}}{3 x^{2}-6}$