Simplify the complex fraction.
-$\frac{a^{-2}-b^{-1}}{7 a^{-1}+3 b^{-2}}$

A) $\frac{a b^{2}-a^{2}}{7 b^{2}+3 a^{2} b}$

B) $\frac{b^{2}-a^{2}}{7 a b^{2}+3 a^{2}}$

C) $\frac{b^{2}-a^{2} b}{7 b^{2}+3 a^{2}}$

D) $\frac{b^{2}-a^{2} b}{7 a b^{2}+3 a^{2}}$

Question

Simplify the complex fraction.
-$\frac{a^{-2}-b^{-1}}{7 a^{-1}+3 b^{-2}}$

A) $\frac{a b^{2}-a^{2}}{7 b^{2}+3 a^{2} b}$

B) $\frac{b^{2}-a^{2}}{7 a b^{2}+3 a^{2}}$

C) $\frac{b^{2}-a^{2} b}{7 b^{2}+3 a^{2}}$

D) $\frac{b^{2}-a^{2} b}{7 a b^{2}+3 a^{2}}$

Quizplus · Accepted Answer

To simplify the complex fraction, first rewrite the negative exponents as positive: $\frac{\frac{1}{a^2} - \frac{1}{b}}{\frac{7}{a} + \frac{3}{b^2}}$. Then, find a common denominator for the numerator and the denominator separately. For the numerator, it's $a^2b$, and for the denominator, it's $ab^2$. Simplifying gives $\frac{b - a^2b}{7b^2 + 3a^2}$, which matches option D.

Simplify the Complex Fraction a−2−b−17a−1+3b−2\frac{a^{-2}-b^{-1}}{7 a^{-1}+3 b^{-2}}7a−1+3b−2a−2−b−1​ A) ab2−a27b2+3a2b\frac{a b^{2}-a^{2}}{7 b^{2}+3 a^{2} b}7b2+3a2bab2−a2​

Simplify the Complex Fraction $\frac{a^{-2}-b^{-1}}{7 a^{-1}+3 b^{-2}}$ A) $\frac{a b^{2}-a^{2}}{7 b^{2}+3 a^{2} b}$