Question

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

Answer 1

Answer:

Value of $x = \frac{1-ab}{a+b}$

Step-by-step explanation:

Given that: $\frac{1}{abx} = \frac{1}{a} +\frac{1}{b} +\frac{1}{x}$

Solve for x;

Taking LCM of a , b and x is abx.

$\frac{1}{abx} =\frac{bx+ax+ab}{abx}$

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;

$x = \frac{1-ab}{a+b}$

Therefore, value of x is; $\frac{1-ab}{a+b}$