SOLUTION: The denominator of a fraction is an integer that is 4 more than the square of the numerator. if the fraction is reduced to lowest terms, it equals 3/20. find the numerator

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Question 230130: The denominator of a fraction is an integer that is 4 more than the square of the numerator. if the fraction is reduced to lowest terms, it equals 3/20. find the numerator
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

To get rid of the fractions we will multiply by the Lowest Common Denominator (LCD). The LCD here is: 20(4+x^2).

Cancel common factors on each side:

leaving:

or

Since this is a quadratic equation, we will get one side equal to zero:

... then factor it (or use the quadratic formula):

From the Zero Product Property we know that this (or any) product can be zero only if one (or more) of the factors is zero. So:
or
Solving these we get:
or
or

Since the problem specifies integers, we must reject x = 2/3. So the only answer to the problem is x=6.
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