Simplify.
-$$\frac { 3 x ^ { - 1 } + 9 y ^ { - 1 } } { 4 x ^ { - 2 } + 3 y ^ { - 2 } }$$
A) $\frac { - 3 x y ^ { 2 } - 9 x ^ { 2 } y } { - 4 y ^ { 2 } + 3 x ^ { 2 } }$
B) $\frac { 4 y ^ { 2 } + 3 x ^ { 2 } } { 3 x y ^ { 2 } + 9 x ^ { 2 } y }$
C) $\frac { 3 x y ^ { 2 } + 9 x ^ { 2 } y } { 4 y ^ { 2 } + 3 x ^ { 2 } }$
D) $\frac { 4 x ^ { 2 } + 3 y ^ { 2 } } { 3 x + 9 y }$

Question

Quizplus · Accepted Answer

To simplify the given expression, we first convert the negative exponents to positive by moving them to the opposite part of the fraction. This gives us: $$\frac{3/x + 9/y}{4/x^2 + 3/y^2}$$ Multiplying numerator and denominator by $x^2y^2$ to clear the denominators, we get: $$\frac{3x^2y^2/x + 9x^2y^2/y}{4x^2y^2/x^2 + 3x^2y^2/y^2}$$ Simplifying, we obtain: $$\frac{3xy^2 + 9x^2y}{4y^2 + 3x^2}$$ which matches choice C.

Simplify - 3x−1+9y−14x−2+3y−2\frac { 3 x ^ { - 1 } + 9 y ^ { - 1 } } { 4 x ^ { - 2 } + 3 y ^ { - 2 } }4x−2+3y−23x−1+9y−1​

Simplify
- $\frac { 3 x ^ { - 1 } + 9 y ^ { - 1 } } { 4 x ^ { - 2 } + 3 y ^ { - 2 } }$