Question

1/(a-1) + 1/b = c

solve for a

Answer 1

as with all fractions, multiply top and bottom by the GCD (a-1)(b) to get

1/(a-1) + 1/b = c
b + (a-1) = c(a-1)(b)
b + a - 1 = abc - bc
a - abc = 1 - b - bc
a = (1-b-bc)/(1-bc) = 1 + b/(bc-1)