Question

How do you simplify $ \dfrac{{1 + \dfrac{1}{x}}}{{5 - \dfrac{1}{y}}} $ ?

Answer 1

Hint: In the given question, we are required to simplify an algebraic expression given to us in the problem. So, we add and subtract the like terms so as to simplify the algebraic expression. We can use algebraic rules and properties in order to simplify the given algebraic expression.

Complete step-by-step answer:
We would use the BODMAS rule in order to simplify the algebraic expression $ \dfrac{{1 + \dfrac{1}{x}}}{{5 - \dfrac{1}{y}}} $ . BODMAS is an acronym for the sequence in which the mathematical operations are to be done. In BODMAS, B stands for brackets, O stands for of, D stands for division, M stands for multiplication, A stands addition, S stands subtraction.
So, $ \dfrac{{1 + \dfrac{1}{x}}}{{5 - \dfrac{1}{y}}} $
So, in order to simplify the numerator and denominator, we need to take LCM of the expressions in numerator and denominator.
 $ \Rightarrow \dfrac{{\dfrac{x}{x} + \dfrac{1}{x}}}{{\dfrac{{5y}}{y} - \dfrac{1}{y}}} $
 $ \Rightarrow \dfrac{{\left( {\dfrac{{x + 1}}{x}} \right)}}{{\left( {\dfrac{{5y - 1}}{y}} \right)}} $
 $ \Rightarrow \dfrac{{y\left( {x + 1} \right)}}{{x\left( {5y - 1} \right)}} $
Opening the brackets in numerator and denominator, we get,
 $ \Rightarrow \dfrac{{xy + y}}{{5xy - x}} $
Hence, the expression $ \dfrac{{1 + \dfrac{1}{x}}}{{5 - \dfrac{1}{y}}} $ can be simplified as $ \dfrac{{xy + y}}{{5xy - x}} $ using the BODMAS rule.
So, the correct answer is “ $ \dfrac{{xy + y}}{{5xy - x}} $ ”.

Note: The given problem deals with algebraic expression. There is no fixed way of simplifying a given algebraic expression. Care should be taken while doing the calculation steps. Algebraic identities and rules may also be used as and when required as they help simplify complex and tedious tasks. Nowadays, another acronym PEMDAS is also coming into use for describing the sequence of arithmetic operations.