Can someone help me in detail showing their steps to get the answer to this problem:
Here's a Hint:
$\displaystyle \frac{{y - \dfrac{{5y - 7}}
{7}}}
{{\dfrac{6}
{{14}} + \dfrac{3}
{{2y}}}} = \frac{{14\left( {y - \dfrac{{5y - 7}}
{7}} \right)}}
{{14\left( {\dfrac{6}
{{14}} + \dfrac{3}
{{2y}}} \right)}}.$
Can you see that it is easier now?
Hello, fluffy_penguin!
Use any method to simplify the complex fraction.
$\displaystyle \frac{y - \frac{5y-7}{7}}{\frac{6}{14} - \frac{3}{2y}}$
Multiply top and bottom by the LCD, $\displaystyle 14y$
$\displaystyle \frac{14y\left(y - \frac{5y-7}{7}\right)}{14y\left(\frac{6}{14} - \frac{3}{2y}\right)} \;=\;\frac{14y\cdot y \:- \:14y\cdot\frac{5y-7}{7}}{14y\cdot\frac{6}{14} \:- \:14y\cdot\frac{3}{2y}} \;= \;\frac{14y - 2y(5y-7)}{6y - 7\cdot3}$
. . $\displaystyle =\;\frac{14y^2 - 10y^2 + 14y}{6y-21} \;= \;\frac{4y^2+14y}{6y-21} \;=\;\frac{2y(2y + 7)}{3(2y-7)}$