Question

How do you evaluate $\dfrac{2}{{3{u^2}w}} - \dfrac{5}{{6u{w^2}}}$?

Answer 1

Hint: In the given question, we have been asked to solve a linear equation with two variables. Since, exponents in denominators have made the expression complicated; we can simplify it by removing the fraction part. Fraction can be removed by replacing the variable with another variable and then solving it. Also, if the fraction is in improper form then convert it into mixed fraction. Improper fraction is when numerator is greater than denominator whereas proper fraction is when numerator is smaller than denominator.

Complete step by step solution:
We are given,
$ \Rightarrow \dfrac{2}{{3{u^2}w}} - \dfrac{5}{{6u{w^2}}}$
We’ll simplify the equation by replacing the variables in denominator by another variable to remove fraction.,
$\dfrac{1}{u} = a$ and $\dfrac{1}{w} = b$
$ \Rightarrow \dfrac{2}{3}({a^2}b) - \dfrac{5}{6}(a{b^2})$
To simplify it further, we’ll take $\dfrac{1}{6}$common
$ \Rightarrow \dfrac{1}{6}[4({a^2}b) - 5(a{b^2})]$
To simplify we’ll pull out the common terms from the expression
\[ \Rightarrow \dfrac{{ab}}{6}(4a - 5b)\]
Now replace the current variables with the original ones.
$ \Rightarrow \dfrac{1}{{6uw}}(\dfrac{4}{u} - \dfrac{5}{w})$

Note: Operations such as addition, subtraction, multiplication and division can only be performed on like terms. To solve questions which have two variables, keep in mind to solve them separately i.e. perform operation on coefficients of the same variable. We also need to take the power of variables; variables with the same power can only be added or subtracted. Also fractions cannot be operated if they have different denominators. Denominators have to be made the same by taking LMC to further operate them. Also, while dealing with fractions we can multiply or divide the numerator and denominator by the same number, the value remains the same.