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Example 1
$\dfrac{6}{3x-6}-\dfrac{1}{x-2} = ?$
- $\dfrac{5}{3x-6}$
- $\dfrac{1}{x-2}$
- $\dfrac{5}{x-2}$
- $\dfrac{3}{x}$
- $\dfrac{5}{x-2}$
Solution
- From the 5 possible answers, we understand that we need to simplify the given expression.
We need to find a common denominator to the two rational expressions in order to subtract them. Note that the first denominator can be written in terms of the second denominator as follows: $3x-6=3(x-2)$. Hence
$\dfrac{6}{3x-6}-\dfrac{1}{x-2}=\dfrac{6}{3(x-2)}-\dfrac{1}{x-2}$
- We now simplify first term
$=\dfrac{3\cdot2}{3(x-2)}-\dfrac{1}{x-2}$
$=\dfrac{\colorcancel{red}{3}\cdot2}{\colorcancel{red}{3}(x-2)}-\dfrac{1}{x-2}$
$=\dfrac{2}{x-2}-\dfrac{1}{x-2}$
$=\dfrac{1}{x-2}$
Answer B
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