Answer:
Value of [tex]x = \frac{1-ab}{a+b}[/tex]
Step-by-step explanation:
Given that: [tex]\frac{1}{abx} = \frac{1}{a} +\frac{1}{b} +\frac{1}{x}[/tex]
Solve for x;
Taking LCM of a , b and x is abx.
[tex]\frac{1}{abx} =\frac{bx+ax+ab}{abx}[/tex]
Multiply both sides by abx we get;
[tex]1 = bx+ax+ab[/tex]
Subtract ab from both sides we get;
1-ab = bx + ax
Using distributive property: [tex]a\cdot (b+c) = a\cdot b +a \cdot c[/tex]
1- ab = x(a + b)
Divide both sides by a+b we get;
[tex]x = \frac{1-ab}{a+b}[/tex]
Therefore, value of x is; [tex]\frac{1-ab}{a+b}[/tex]
