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

Answer 1

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

My most basic Method (Then the details of this particular equation beside the step)

Step 1: cross multiply to get y(y+5) = 3(y+8)

Step 2: Perform the functions of each side so that you can get variables that can eventually be added or subtracted so that you get y²+5y = 3y+24.

Step 3: Bring everything to one side and make it = "0' to look like this:

y² + 5y - 3y - 24 = 0

y² + 2y - 24 = 0

Step 4: Find two factors that = the left side and then solve the variable in each of the factors to give the parabolic y intercepts (if you are required to do so on a graph). It now looks like this: (y+6)(y-4) = 0

y+6 = 0

y-4 = 0

Therefore,

y= -6

and

y = 4

Then you can check to make sure both these work by inserting them into your original equation which by my calculations, they work (make sure when substituting each, you only substitute one at a time when checking your work otherwise, the checking step will not work).

Answer 2

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 3

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