Question

If a ≠ b and 1/x + 1/a = 1/b, then x = A. 1/b - 1/a. B. b - a. C. 1/ab. D. a - b/ab. E. ab/a - b.

Answer 1

E

Explanation:

given

`(1)/(x)` +
`(1)/(a)` =
`(1)/(b)` ( combine fractions on left side )

`(a+x)/(ax)` =
`(1)/(b)` ( cross- multiply )

ax = b(a + x) ← distribute parenthesis by b

ax = ab + bx ( subtract bx from both sides )

ax - bx = ab ← factor out x from each term on the left side

x(a - b) = ab ← divide both sides by (a - b )

x =
`(ab)/(a-b)`