Chapter 12.6, Problem 6MRE

To determine

To calculate: The values of y .

Answer to Problem 6MRE

The values of y are $8\text{ and }-2$ .

Explanation of Solution

Given information:

Equation is given as, $y-\frac{7}{y+2}-\frac{3y-1}{y+2}=5$

Consider the given equation as, $y-\frac{7}{y+2}-\frac{3y-1}{y+2}=5$

Now,

  $\begin{array}{c}y-\frac{7}{y+2}-\frac{3y-1}{y+2}=5\\ \frac{y\left(y+2\right)-7-\left(3y-1\right)}{y+2}=5\\ y\left(y+2\right)-7-\left(3y-1\right)=5\left(y+2\right)\\ y^2+2y-7-3y+1=5y+10\end{array}$

On further solving,

  $\begin{array}{c}{y}^2-y-6-5y-10=0\\ y^2-6y-16=0\\ y^2-\left(8-2\right)y-16=0\\ y^2-8y+2y-16=0\\ y\left(y-8\right)+2\left(y-8\right)=0\\ \left(y-8\right)\left(y+2\right)=0\\ y=8,-2\end{array}$

Therefore, the values of y are $8\text{ and }-2$ .