Example Question 6

Example corresponding to question 6 in algebra_4.

Example 1


$\dfrac{6}{3x-6}-\dfrac{1}{x-2} = ?$

  1. $\dfrac{5}{3x-6}$


  2. $\dfrac{1}{x-2}$


  3. $\dfrac{5}{x-2}$


  4. $\dfrac{3}{x}$


  5. $\dfrac{5}{x-2}$

Solution


  1. 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

    $\dfrac{6}{3x-6}-\dfrac{1}{x-2}=\dfrac{6}{3(x-2)}-\dfrac{1}{x-2}$

  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