Simplify the expression. $\frac { 1 } { a } - \frac { 2 } { a ^ { 2 } b } + \frac { 1 } { b ^ { 2 } }$
A) $\frac { b ^ { 2 } - 3 a b + 4 a ^ { 2 } } { 2 a ^ { 2 } b ^ { 2 } }$
B) $\frac { b - 3 a b + 2 a } { 2 a b }$
C) $\frac { b ^ { 2 } - 3 a b + 6 a ^ { 2 } } { 3 a ^ { 2 } b ^ { 2 } }$
D) $\frac { a b ^ { 2 } - 2 b + a ^ { 2 } } { a ^ { 2 } b ^ { 2 } }$
E) $\frac { a b ^ { 2 } - 3 a b + 2 a ^ { 2 } b } { a ^ { 3 } b ^ { 3 } }$

Question

Quizplus · Accepted Answer

To simplify this expression, we need to find a common denominator first. One way to do this is to multiply the first term by $b^2/b^2$ and the second term by $a/b$, so that we have:

$$\frac{b^2}{ab^2} - \frac{2a}{a^2b^2} + \frac{1}{b^2}$$

Combining the terms, we get:

$$\frac{a b ^2 - 2 b + a ^ { 2 }} { a ^ { 2 } b ^ { 2 }}$$

which is equivalent to choice D.

Simplify the Expression 1a−2a2b+1b2\frac { 1 } { a } - \frac { 2 } { a ^ { 2 } b } + \frac { 1 } { b ^ { 2 } }a1​−a2b2​+b21​

Simplify the Expression $\frac { 1 } { a } - \frac { 2 } { a ^ { 2 } b } + \frac { 1 } { b ^ { 2 } }$