Question

How do you simplify $\dfrac{{3x + 12}}{{x + 4}}$?

Answer 1

Hint: Given an expression in fraction form. We have to simplify the expression. First, we will solve the numerator by taking out the common term from the numerator. Then, we will cancel out the terms which are common in the numerator and denominator. Then, write the expression in simplified form.

Complete step-by-step answer:
We are given the expression $\dfrac{{3x + 12}}{{x + 4}}$. First, we will write $12$ in factored form.
$ \Rightarrow \dfrac{{3x + 3 \times 4}}{{x + 4}}$
Now, we will take out $3$ as a common term from the numerator.
$ \Rightarrow \dfrac{{3\left( {x + 4} \right)}}{{x + 4}}$
Now, numerator and denominator contain the common term, $x + 4$. Now, we will cancel out the common terms from the numerator and denominator.
$ \Rightarrow \dfrac{{3l{{\left( {x + 4} \right)}}}}{{l{{x + 4}}}}$
On simplifying the expression, we get:
$ \Rightarrow 3$

Thus, the solution of the expression is $\dfrac{{3x + 12}}{{x + 4}} = 3$

Additional information: The expression which is in fraction form, must be solved by cancelling out the common factor from the numerator and denominator. The linear equation can be solved by taking out the common term and writing it in simplified form. The expression contains a linear equation in the numerator and denominator. The denominator shows that there is no common term to take out. So, it is already in reduced form. Then, try to factor the numerator if possible. Otherwise, the solution is determined by the long division method.

Note:
In such types of questions students mainly don't get an approach on how to solve it. In such types of questions, students are mainly confused about which operation is applied to simplify the fraction. Students may forget to check whether the factors of the numerator or denominator is possible to reduce the expression.