Question

How do you solve for x in the equation $\dfrac{1}{x} - \dfrac{1}{a} = \dfrac{1}{b}$ ?

Answer 1

Hint:In this question, we are given an algebraic expression containing three unknown variable quantities. We know that we need an “n” number of equations to find the value of “n” unknown variables. Although we have three unknown quantities, we are given that we have to solve for x, so we assume a and b to be some unknown constant values. So, in the given algebraic expression, we have 1 unknown quantity and exactly one equation to find the value of x. For that, we will rearrange the equation such that x lies on the one side of the equation and all other terms lie on the other side. Then by applying the given arithmetic operations, we can find the value of x.

Complete step by step answer:
We are given that $\dfrac{1}{x} - \dfrac{1}{a} = \dfrac{1}{b}$
Taking $\dfrac{1}{a}$ to the right-hand side of the equation, we get –
$\dfrac{1}{x} = \dfrac{1}{b} + \dfrac{1}{a}$
Taking LCM of the denominators, we get –
$\dfrac{1}{x} = \dfrac{{a + b}}{{ab}}$
Reciprocating both the sides, we get –
$x = \dfrac{{ab}}{{a + b}}$
Hence, when $\dfrac{1}{x} - \dfrac{1}{a} = \dfrac{1}{b}$ , we get $x = \dfrac{{ab}}{{a + b}}$ .

Note: As the given equation combines the numerical values and alphabets via arithmetic operations like addition, subtraction, multiplication and division, so the given expression is an algebraic expression. the alphabets, x, a and b represent some unknown quantities. In the answer, we have got as a fraction in terms of a and b, so the value of x depends on the value of a and b. On putting the values of a and b, we will get the value of x.