y/3 = (y+8)/(y+5)

Answer 1

y/3=(y+8)/(y+5)

cross Multiplication

y(y+5)=3(y+8)

Evaluate parehthesis by multiplying by "y" on L.H.S and by "3"on R.H.S.

y2+5y=3y+24

Placing the R.H.S. value on L.H.S.

y2+5y-3y-24=0

y2+2y-24=0

y2+6y-4y-24=0

y(y+6)-4(y+6)=0

(y-4)(y+6)=0

(y-4)=0 ,(y+6)=0

y=4, y=-6

Answer 2

We cross-multiply and solve, checking that the solution is not y = -5.

y^2 + 5y = 3y + 24

y^2 + 2y - 24 = 0

(y-6)(y+4) =0

y = -6, 4