Question

solve \\(\frac{1}{2} + \frac{1}{2x} = \frac{x^2 - 7x + 10}{4x}\\) by rewriting the equation as a proportion. which proportion is equivalent to the original equation? \\(\circ\\) \\(\frac{x + 2}{2x} = \frac{x^2 - 7x + 10}{4x}\\) \\(\circ\\) \\(\frac{x - 1}{2x} = \frac{x^2 - 7x + 10}{4x}\\) \\(\circ\\) \\(\frac{x + 1}{2x} = \frac{x^2 - 7x + 10}{4x}\\)

Explanation:

Step1: Combine left-hand side fractions

Find a common denominator ($2x$) for $\frac{1}{2} + \frac{1}{2x}$:
$\frac{1}{2} = \frac{x}{2x}$, so $\frac{x}{2x} + \frac{1}{2x} = \frac{x+1}{2x}$

Step2: Match to the equation

Set the combined fraction equal to the right-hand side of the original equation:
$\frac{x+1}{2x} = \frac{x^2 -7x +10}{4x}$

Answer:

$\boldsymbol{\frac{x+1}{2x} = \frac{x^2 -7x +10}{4x}}$ (the third option)