What is the solution of -8/2y-8=5/y+4 - 7y+8/y^2-16? y = –4 y = –2 y = 4 y = 6

Please clarify whether you meant (-8/2)y or   -8 / (2y - 8).

It's always a good idea to use parentheses for clarity; it reduces or removes the need for guessing.

Here is my interpretation of your equation:

-8/2y-8=5/y+4 - 7y+8/y^2-16  becomes

-8 / (2y-8) = 5 / (y+4) - 7y + 8 / (y^2-16)   (note use of parentheses)

Factoring all of the denominators results in:

-8 / [2(y-4)] = 5 / (y+4) - 7y  + 8 / [(y-4)(y+4)]

The LCD is 2(y-4)(y+4).  You must multiply each and every term in the above equation by this LCD to clear fractions:

-8(y+4) = 5(2)(y-2) - 7(y+4)(y-4) + 8/2

Then -8y - 32 = 10y -20 -7y^2 + 4

I believe the "-7y^2" term is incorrect.

In retrospect, you could simply substitute each of the given answers (y-values), one at a time, to determine which, if any, makes the equation true:

-8 / (2y-8) = 5 / (y+4) - 7y + 8 / (y^2-16)   (note use of parentheses)

Let's test y = 4.  Is this a solution?  Subst. 4 for y in the above equation, we get:

-8 / (8-8) and several more terms.  No, 4 is not a solution, because 
-8 / (0) is undefined.  Eliminate y = 4 as a solution.  Try y = -4 and the other given possible solutions.  Do any of them make this equation true?

1. isolate the variable, in this case, d. subtract 35.5 on both sides of the equation.2. 52 subtracted by 35.5 is 16.53. therefore your answer would be d= 16.5this is the basics of pre algebra, isolating variable through adding, subtracting, multiplying, and dividing, if you have any other questions to ask just comment!