how would i solve this problem or a problem similar a= 1/x+1/a=1/b, then x=

Question

I am horrible at algebra and fractions. I am trying to pass a placement test for college....please help

Answer 1

a = 1/b = 1/x + 1/a

1/x + 1/1/b = 1/x + b = 1/b

1/x = 1/b -b = 1/b - b^2/b = (1-b^2)/b

x = b/(1-b^2)

or

a = 1/x + 1/a

1/x = a - 1/a = a^2/a - 1/a = (a^2- 1)/a

x = a/(a^2-1)