Simplify Help Please

[Samara]

I know the answer to this problem, however, I am unsure of how to reach the solution. If someone could please guide be through it, I would greatly appreciate it!


Thank you!

 

[soroban]

Hello, Samara!

\(\displaystyle \dfrac{4 + \frac{2}{x}}{\frac{x}{4} + \frac{1}{8}}\)

When we are given a complex fraction (one with more than two "levels"),
. . multiply numerator and denominator by the common denominator of all the denominators.

The denominators are \(\displaystyle 1, x, 4, 8\). .The common denominator is \(\displaystyle 8x.\)

We have: .\(\displaystyle \dfrac{8x\left(4 + \frac{2}{x}\right)}{8x\left(\frac{x}{4} + \frac{1}{8}\right)} \;=\; \dfrac{32x + 16}{2x^2 + x} \;=\;\dfrac{16(2x+1)}{x(2x+1)} \;=\;\dfrac{16}{x} \)

 

[Samara]

Thank you for your assistance! This makes it much easier to understand!