(y- 8)+ (1/y-8) please HELP!?

Question

(y-8) + (1 /y-8)
I got y-8 / 1

Im not sure please heLPP!!
Thankyou very very much

Answer 1

if by this you mean

(y - 8) + (1/(y - 8))

Multiply everything by (y - 8)

((y - 8)^2 + 1)/(y - 8)
(((y - 8)(y - 8)) + 1)/(y - 8)
((y^2 - 8y - 8y + 64) + 1)/(y - 8)
(y^2 - 16y + 64 + 1)/(y - 8)
(y^2 + 16y + 65)/(y - 8)

Answer 2

(y - 8) + 1/(y - 8)

Your first step is to put them under a common denominator.

[(y - 8)^2] / (y - 8) + 1 / (y - 8)

Now, merge the two fractions.

{[y - 8]^2 + 1} / (y - 8)

Expand the numerator.

(y^2 - 16y + 64 + 1) / (y - 8)

(y^2 - 16y + 63) / (y - 8)
(y - 9)(y - 7) / (y - 8)

Answer 3

(y- 8)+ (1/y-8) = (y-8) +((1-8y)/y) = (y^2 - 8y)/y + (1 - 8y)/y = (y^2 -8y + 1 - 8y)/y = (1/y)*(y^2 - 16y +1)