Answer
$y=\left\{ 1,\dfrac{11}{4} \right\}$
Work Step by Step
Multiplying both sides by the $LCD=
4y+1
,$ then the solution to the given equation, $
\dfrac{-15}{4y+1}+4=y
,$ is
\begin{array}{l}\require{cancel}
1(-15)+(4y+1)(4)=(4y+1)(y)
\\\\
-15+16y+4=4y^2+y
\\\\
-4y^2+16y-y-15+4=0
\\\\
-4y^2+15y-11=0
\\\\
4y^2-15y+11=0
\\\\
(4y-11)(y-1)=0
\\\\
y=\left\{ 1,\dfrac{11}{4} \right\}
.\end{array}
