Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { \frac { 5 } { x - h } + \frac { 5 } { x } } { 2 x - h }$$
A) $h$
B) $\frac { 5 } { x ( x - h ) }$
C) $\frac { 5 } { x ( x + h ) }$
D) $\frac { 1 } { x ( x - h ) }$

Question

Quizplus · Accepted Answer

To simplify the given expression, first find a common denominator for the fractions in the numerator, which is $x(x-h)$. This gives us $\frac{5x + 5(x-h)}{x(x-h)}$ divided by $2x-h$. Simplifying the numerator gives $\frac{5x + 5x - 5h}{x(x-h)}$, which simplifies further to $\frac{10x - 5h}{x(x-h)}$. Dividing by $2x-h$ is the same as multiplying by its reciprocal, so we get $\frac{10x - 5h}{x(x-h)(2x-h)}$. However, the correct simplification aligns with option B, which indicates a simplification error in the step-by-step explanation. The correct initial approach should involve combining the fractions in the numerator correctly and simplifying the entire expression properly, leading to $\frac{5}{x(x-h)}$, without unnecessary steps that might have introduced errors.

Write the Expression with Only Positive Exponents and Evaluate If 5x−h+5x2x−h\frac { \frac { 5 } { x - h } + \frac { 5 } { x } } { 2 x - h }2x−hx−h5​+x5​​

Write the Expression with Only Positive Exponents and Evaluate If $\frac { \frac { 5 } { x - h } + \frac { 5 } { x } } { 2 x - h }$