Question

What is the solution of StartFraction negative 8 Over 2 y minus 8 EndFraction = StartFraction 5 Over y + 4 EndFraction minus StartFraction 7 y + 8 Over y squared minus 16 EndFraction?

1. Giakhanh
The solution of the fraction given as -8/(2y – 8) = 5/(y + 4) – (7y + 8)/(y² – 16) is determined as 4 or – 0.25.

### What is fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts.
A fraction  can also be described as how many parts of a certain size there are, in a given whole.

### Solution of the fraction

The fraction given can be written as follows;
-8/(2y – 8) = 5/(y + 4) – (7y + 8)/(y² – 16)

### simplify as follows;

-8/(2y – 8) = 5/(y + 4) – (7y + 8)/(y – 4)(y+4)
-8/(2y – 8)  = [5(y – 4) – (7y + 8)] /(y-4)(y + 4)
-8/(2y – 8)  = (5y – 20 + 7y + 8)/(y-4)(y + 4)
-8/(2y – 8)  = (12y – 12)/(y-4)(y + 4)
cross and multiply both sides of the equation;
-8((y-4)(y + 4)) = (12y – 12)(2y – 8)
-8(y² – 16) = 24y² – 96y – 24y + 96
-8y² + 128 =  24y² – 120y + 96
0 = 32y² – 120y – 32
solve the quadratic equation using formula method;
a = 32, b = -120, c = – 32
y = 4 or -0.25
Thus, the solution of the fraction given as -8/(2y – 8) = 5/(y + 4) – (7y + 8)/(y² – 16) is determined as 4 or – 0.25.