Math CentralQuandaries & Queries


Question from Farina, a student:

how do i simplify (1/3 + 1/3x) / (1/x + x/3x)

Hi Farina,

I would start by dealing with the numerator and denominator separately. The numerator is

1/3 + 1/(3x)

To add these two fractions you need to find a common denominator. If you multiply the numerator and denominator of the first fraction by x then it will have a denominator of 3x, the same denominator as the second fraction. Thus

1/3 + 1/(3x)
= (1 times x)/(3 times x) + 1/(3x)
= x/(3x) + 1/(3x)
= (x + 1)/(3x)

Now look at the denominator of the original fraction

1/x + x/(3x)

Find a common denominator and add the two fractions. Put the original problem back together and simplify.

I hope this helps,

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