Question

Solve for x:
1/abx = 1/a + 1/b + 1/x

Answer 1

Value of
`x = (1-ab)/(a+b)`

Explanation:

Given that:
`(1)/(abx) = (1)/(a) +(1)/(b) +(1)/(x)`

Solve for x;

Taking LCM of a , b and x is abx.

`(1)/(abx) =(bx+ax+ab)/(abx)`

Multiply both sides by abx we get;

`1 = bx+ax+ab`

Subtract ab from both sides we get;

1-ab = bx + ax

Using distributive property:
`a\cdot (b+c) = a\cdot b +a \cdot c`

1- ab = x(a + b)

Divide both sides by a+b we get;

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

Therefore, value of x is;
`(1-ab)/(a+b)`