I hate math!!!!I need helppppppppp,plez?

Question

How in the world do I solve this.....

(y over y-8) + (y over y^2 -64) = (y+9 over y+8)

( )= fractions

Answer 1

You need to multiply the whole equation by the denominators.
However, please note that since (a^2 - b^2) = (a + b)(a - b), that (y^2 - 64) = (y + 8)(y - 8), so...

(y + 8)*y + y = (y + 9)(y - 8)

(This is after multiplying equation by (y+8)(y-8))

y^2 + 8y + y = y^2 - 8y + 9y -72
8y = -72
y = -9

Answer 2

(y^2 - 64) factors into (y+8)(y-8), which is your lowest common denominator. Multiplying everything by this gives you the following:

y(y+8) + y = (y+9)(y-8)
y^2 + 9y = y^2 + y - 72
9y = y - 72
8y = -72
y = -9

Answer 3

y^2 - 64 = (y - 8)(y + 8), so y^2 - 64 is your common denominator.
Multiplying through by (y - 8)(y + 8) you have
y(y - 8)(y + 8)/(y - 8) + y(y - 8)(y + 8)/(y - 8)(y + 8) = (y + 9)(y - 8)(y + 8)/(y + 8)
Cancelling like terms leaves you with
y(y + 8) + y = (y + 9)(y - 8)
Expanding,
y^2 + 8y + y = y^2 + y - 72
"collecting" terms,
y^2 - y^2 + 8y + y - y = - 72
8y = - 72
Dividing through by 8,
y = - 9

Answer 4

y/(y-8) + y/((x-8)(x+8) = (y+9)/(y+8)

common denominator is (y - 8)(y+8)

(y(y+8) + y - (y+9)(y-8))/((y-8)(y+8) = 0

for this to be true
(y - 8)(y + 8) not = 0
y not = 8
y not = -8

we can eliminate the denominator now
y(y+8) + y - (y + 9)( y - 8) = 0
y^2 + 8y + y - y^2 - 8y + 9y - 72 = 0
10 y = 72
y = 7.2

Answer 5

multiply the entire problem by the lowest common denominator, (x-8)(x+8). that should simplify it so its easier to solve.