Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$$
A) $\frac { 16 } { x }$
B) $\frac { x } { 16 }$
C) 16
D) 1

Question

Quizplus · Accepted Answer

To simplify the given expression, first find a common denominator for the fractions in both the numerator and the denominator of the complex fraction. The expression is $$\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$$. Multiply the numerator and the denominator by $8x$ to eliminate the fractions: $$\frac { (4 + \frac { 2 } { x }) \cdot 8x } { (\frac { x } { 4 } + \frac { 1 } { 8 }) \cdot 8x }$$ which simplifies to $$\frac { 32x + 16 } { 2x^2 + x }$$. Factoring out $x$ from the denominator gives $$\frac { 32x + 16 } { x(2x + 1) }$$. The expression simplifies to $\frac { 16 } { x }$ when further simplified, as there's no common factor to cancel out with $x$ in the denominator.

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Write the Expression with Only Positive Exponents and Evaluate If $\frac { 4 + \frac { 2 } { x } } { \frac { x } { 4 } + \frac { 1 } { 8 } }$