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How do you simplify \[\dfrac{3x-6}{x-2}\]?

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Last updated date: 01st Mar 2024
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IVSAT 2024
Answer
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Hint: This type of problem can be solved by finding the common terms. First, we have to consider the given function with variable x and compare the numerator and denominator. There is a common term in the numerator that is 3. Take the common term out of the bracket. Then, we get x-2 common in both the numerator and denominator. On cancelling the common term from the numerator and denominator, we get a simplified form of the equation which is the required answer.

Complete step by step answer:
According to the question, we are asked to simplify \[\dfrac{3x-6}{x-2}\].
 We have been given the function \[\dfrac{3x-6}{x-2}\]. ---------(1)
Let us first consider the numerator 3x-6.
We know that 6 is the product of 3 and 2.
On simplifying 6 from the numerator, we get
\[\Rightarrow 3x-6=3x-3\times 2\]
Here, 3 are common in both the terms.
On taking 3 common out of the bracket, we get
\[3x-6=3\left( x-2 \right)\]
Let us now substitute the simplified form of the numerator in the function (1).
Therefore, we get
\[\dfrac{3x-6}{x-2}=\dfrac{3\left( x-2 \right)}{x-2}\]
We find that x-2 is common in both the numerator and denominator.
Let us cancel out x-2 from the numerator and denominator.
We get,
\[\Rightarrow \dfrac{3x-6}{x-2}=\dfrac{3}{1}\]
We know that any term divided by 1 is equal to the term itself.
Therefore, we get
\[\dfrac{3x-6}{x-2}=3\]

Hence, the simplified form of the function \[\dfrac{3x-6}{x-2}\] is 3.

Note: Whenever we get such types of problems, we should always compare the numerator and denominator. Look for the common terms which can be a variable or a constant. We should first take the common term out of the bracket and then, we should proceed with cancelling the common terms from the numerator and denominator. Avoid calculation mistakes based on sign conventions.
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