If sqrt(6y + 2)/sqrt(2y + 2) = 5/2, solve for y. Express your answer in simplest fractional form.
I am going to assume we are looking nly for real solutions.
sqrt(6y + 2)/sqrt(2y + 2) = 5/2
\(\displaystyle \frac{\sqrt{(6y + 2)}}{\sqrt{(2y + 2)}} = \frac{5}{2}\\ \)
First you need to recognize that 2y+2 must be > 0
y > -1
square both sides
\(\displaystyle \frac{(6y + 2)}{(2y + 2)}= \frac{25}{4}\\ \)
Can you take it from there?