Question

How do you simplify the expression \[\dfrac{3x-6}{6}\]?

Answer 1

Hint: In the type of question that has been mentioned above we will have to first differentiate the terms that are there, in the above question the numerator has two terms and the denominator has one so we will differentiate the final function in two parts with the denominator being same and then solve it to give the final value of the function.

Complete step by step solution:
To solve the above question first we are going to understand the basic concept of solving fraction, in the fraction that has been provided to us first we will check in the numerator whether something is common in both the terms, if there is we are going to take it out so as to simplify the numerator, after simplifying the numerator we are going to check whether the values that were taken out as common values from the numerator is a multiple of the value in the denominator or even if a part of it is a multiple of the denominator value (example: if the value taken out in numerator is 8 and the value in the denominator is 12 we can see that both 8 and 12 are a multiple of 4 so we will cancel them out out which will leave 2 in the numerator and 3 in the denominator) with this we will be able to simplify complex terms of fraction into easy terms.
Now in our question in the numerator we can take out 3 and when we check it out with the denominator we can see that 6 is a multiple of 3 so we will cancel out 3 and 6 which will leave out numerator as 1 and denominator as 2 then we will differentiate the terms with variables on one part and constant on other from which we will get:
\[\begin{align}
  & =\dfrac{3\left( x-2 \right)}{6} \\
 & =\dfrac{\left( x-2 \right)}{2} \\
 & =\dfrac{x}{2}-\dfrac{2}{2} \\
 & =\dfrac{x}{2}-1 \\
\end{align}\]
So the simplification of the function stated in the question is \[\dfrac{x}{2}-1\].

Note: In the above type of question always try to take common values so as to simplify the whole equation, the use of simplification is to make clear of many other values example: if after taking common the values in the numerator and denominator becomes same we could be able to five the final answer much faster than before.