Answer:[tex]\frac{\frac{1}{7}+\frac{1}{x}}{\frac{x}{7}-\frac{7}{x}}=\frac{1}{x-7}[/tex]
Explanation:
Given:
[tex]\frac{\frac{1}{7}+\frac{1}{x}}{\frac{x}{7}-\frac{7}{x}}[/tex]
Let us write the numerator as a single fraction, as well as the denominator. This can be written as:
[tex]\frac{\frac{x+7}{7x}}{\frac{x^2-49}{7x}}[/tex]
Division by a fraction may become a mu
[tex]\begin{gathered} \frac{x+7}{7x}\times\frac{7x}{x^2-49} \\ \\ =\frac{x+7}{7x}\times\frac{7x}{(x+7)(x-7)} \\ \\ =\frac{1}{x-7} \end{gathered}[/tex]
