Answer
$(x-5)$
Work Step by Step
Given: $\dfrac{\dfrac{x}{5}-\dfrac{5}{x}}{\dfrac{1}{5}+\dfrac{1}{x}}$
Let us consider the numerator expression
$\dfrac{x}{5}-\dfrac{5}{x}=\dfrac{x^2-25}{5x}$ ...(1)
Now, we will consider the denominator expression.
$\dfrac{1}{5}+\dfrac{1}{x}=\dfrac{x+5}{5x}$ ...(2)
Divide equation (1) by (2).
Hence, $\dfrac{\dfrac{x}{5}-\dfrac{5}{x}}{\dfrac{1}{5}+\dfrac{1}{x}}=\dfrac{x^2-25}{x+5}=\dfrac{(x-5)(x+5)}{x+5}=(x-5)$
