Question

How do you simplify $\dfrac{{2x - 3}}{{1 - 5x}} \times \dfrac{{5x - 1}}{{2x + 3}}$ ?

Answer 1

Hint: In this question, we are given an algebraic expression and we have to simplify it. Understanding the question is also very important. We just have to simplify the expression. We don’t have to find the value of $x$. Start by multiplying the numerator with the numerator and, the denominator with the denominator. Simplify by taking something common. It will simplify your expression and you will have your answer.

Complete step-by-step solution:
We are given an algebraic expression and we have been asked to simplify it.
$ \Rightarrow \dfrac{{2x - 3}}{{1 - 5x}} \times \dfrac{{5x - 1}}{{2x + 3}}$ …. (given)
We will simply multiply the numerator with the numerator and, the denominator with the denominator.
$ \Rightarrow \dfrac{{\left( {2x - 3} \right)\left( {5x - 1} \right)}}{{\left( {1 - 5x} \right)\left( {2x + 3} \right)}}$
If you notice, you will see that there are certain similar terms in the numerator and denominator. In order to make them equal, we will take $ - 1$ common in numerator. (While performing a step in the answer, you need to understand why you are performing that step.)
$ \Rightarrow \dfrac{{\left( {2x - 3} \right) \times - \left( {1 - 5x} \right)}}{{\left( {1 - 5x} \right)\left( {2x + 3} \right)}}$
Now, you will be able to see two like terms in the numerator and the denominator. Cancel them out to simplify the expression. You will get –
$ \Rightarrow \dfrac{{\left( {2x - 3} \right) \times - 1}}{{\left( {2x + 3} \right)}}$
$ \Rightarrow \dfrac{{ - \left( {2x - 3} \right)}}{{\left( {2x + 3} \right)}}$
Opening the brackets,
$ \Rightarrow \dfrac{{ - 2x + 3}}{{2x + 3}}$
Now, since these terms are not identical, they cannot be cancelled or simplified further.

Hence, $\dfrac{{ - 2x + 3}}{{2x + 3}}$ is our required answer.

Note: Did you notice how we are using the word “expression” everywhere and not “equation”? This is because an equation is called so when it has a sign of “equals” (=). But what is given to us does not include any such sign. Therefore, that is why we are referring to the given expression as “expression” and not “equation”.