Question

If x=a/b, a does not equal b, and b does not equal 0, find the value of (a+b)/(a-b) in terms of x

Answer 1

`(x+1)/(x-1)`

Explanation:

given

x =
`(a)/(b)` ( multiply both sides by b )

bx = a

substitute a = bx into the expression

`(a+b)/(a-b)`

=
`(bx+b)/(bx-b)` ← factor out b from each term on the numerator and denominator

=
`(b(x+1))/(b(x-1))` ← cancel b on numerator / denominator

=
`(x+1)/(x-1)`