Answer
The solutions are -1 and 7
Work Step by Step
6+$\frac{5}{y}$=y-$\frac{2}{y}$
y(6+$\frac{5}{y}$)=y(y-$\frac{2}{y}$)
6y+y$\frac{5}{y}$=y*y-y$\frac{2}{y}$
6y+5=$y^{2}$-2
0=$y^{2}$-2-6y-5
0=$y^{2}$-6y-7
0=$y^{2}$+y-7y-7
0=y(y+1)-7(y+1)
0=(y-7)(y+1)
y-7=0 or y+1=0
y=7 or y=-1
The solutions are -1 and 7
Check
Let y=-1
6+$\frac{5}{y}$=y-$\frac{2}{y}$
6+$\frac{5}{-1}$=-1-$\frac{2}{-1}$
6-5=-1+2
1=1
Let y=7
6+$\frac{5}{y}$=y-$\frac{2}{y}$
6+$\frac{5}{7}$=7-$\frac{2}{7}$
$\frac{42}{7}$+$\frac{5}{7}$=$\frac{49}{7}$-$\frac{2}{7}$
$\frac{47}{7}$=$\frac{47}{47}$