Question

Solve 1/x = 1/a + 1/b find x

Answer 1

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

Explanation:

Given

`(1)/(x)` =
`(1)/(a)` +
`(1)/(b)`

Multiply through by abx ( the LCM of denominators ) to clear the fractions

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

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

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

Answer 2

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

Explanation:

Combine the two fractions on the right by using the common denominator ab.

`(1)/(x)=(b)/(ab)+(a)/(ab)\\=(b+a)/(ab)`

If two quantities are equal, then their reciprocals are equal.

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