What is the quotient? n+3/2n-6 divide n+3 /3n-9

Question

What is the quotient? n+3/2n-6 divide n+3 /3n-9

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    0
    2021-09-04T18:47:03+00:00

    ANSWER
    The quotient simplifies to
     \frac{3}{2}

    EXPLANATION

    We want to find the quotient:

     \frac{n + 3}{2n - 6}  \div  \frac{n + 3}{3n - 9}

    We need to multiply the first fraction by the reciprocal of the second fraction to obtain,

    \Rightarrow \frac{n + 3}{2n - 6}  \div  \frac{n + 3}{3n - 9}  =  \frac{n + 3}{2n - 6}   \times  \frac{3n  -  9}{n + 3}

    We now factor to obtain,

    \Rightarrow\frac{n + 3}{2n - 6}  \div  \frac{n + 3}{3n - 9}  =  \frac{n + 3}{2(n - 3)}   \times  \frac{3(n  -  3)}{n + 3}

    We cancel out common factors to obtain,

     \Rightarrow\frac{n + 3}{2n - 6}  \div  \frac{n + 3}{3n - 9}  =  \frac{1}{2}   \times  \frac{3}{1}

    This finally gives us,

     \frac{n + 3}{2n - 6}  \div  \frac{n + 3}{3n - 9}  =  \frac{3}{2}

    0
    2021-09-04T18:47:36+00:00

    (n+3)/(2n-6):(n+3)/(3n-9)=(n+3)/(2(n-3))×(3(n-3))/(n+3)=3/2

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