Question

which expression is equivalent to the following complex fraction?\\(\frac{2 - \frac{1}{y}}{3 + \frac{1}{y}}\\)\\(\bigcirc\\ \frac{3y + 1}{2y - 1}\\)\\(\bigcirc\\ \frac{(2y - 1)(3y + 1)}{y^2}\\)\\(\bigcirc\\ \frac{y^2}{(2y - 1)(3y + 1)}\\)\\(\bigcirc\\ \frac{2y - 1}{3y + 1}\\)

Explanation:

Step1: Simplify numerator to single fraction

$2 - \frac{1}{y} = \frac{2y - 1}{y}$

Step2: Simplify denominator to single fraction

$3 + \frac{1}{y} = \frac{3y + 1}{y}$

Step3: Rewrite as division of fractions

$\frac{\frac{2y - 1}{y}}{\frac{3y + 1}{y}} = \frac{2y - 1}{y} \times \frac{y}{3y + 1}$

Step4: Cancel common factor $y$

$\frac{2y - 1}{\cancel{y}} \times \frac{\cancel{y}}{3y + 1} = \frac{2y - 1}{3y + 1}$

Answer:

$\frac{2y - 1}{3y + 1}$ (the fourth option)