Question

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

Answer 1

Hint: In this question, we are given a term where two different terms are being divided by each other, and we have been asked to simplify the term. We can use two methods to simplify the given term.
Method 1: In this method, we will simply take out $3$ common from the numerator. After taking common, you will notice a similar term in numerator and denominator both. Cancel them out and you will have your answer.
Method 2: If you are not comfortable in handling the division in this way, you can use the usual long division method to find the quotient and remainder. Put $3x + 12$ as the dividend and $x + 4$ as the divisor.

Complete step by step answer:
We will use method 1 to solve the given question.
We are given a term and we have been asked to simplify it.
$ \Rightarrow \dfrac{{3x + 12}}{{x + 4}}$ …. (Given)
Now we can write the terms in the numerator as a product of –
$ \Rightarrow \dfrac{{3 \times x + 3 \times 4}}{{x + 4}}$
Now, we can see that $3$ is common in the numerator. So, I will take out $3$ common from the numerator.
$ \Rightarrow \dfrac{{3\left( {x + 4} \right)}}{{x + 4}}$
Now, we can see terms like numerator and denominator. Next step is to cancel the terms.
$ \Rightarrow 3$
Hence, $\dfrac{{3x + 12}}{{x + 4}} = 3$

Note: Now, I will use the long division method to find the answer of the given term.
We will put $3x + 12$ as the dividend and $x + 4$ as the divisor as shown below:
$x + 4)\overline {3x + 12} $
Now, we have to find such a number which when multiplied by $x$ will give us $3x$. Such a number is $3$. Write $3$ at the place of dividend and multiply the divisor by the quotient and write the product below the dividend and then, subtract as show below:
$\begin{array}{*{20}{c}}
  {{\text{ }}3} \\
  {x + 4)\overline {3x + 12} } \\
  {{\text{ }}3x + 12} \\
  {{\text{ }}\left( - \right)} \\
  {{\text{ }}\overline {{\text{ }}0} }
\end{array}$
Hence, our quotient is $3$.