Question 230130
{{{x/(4+x^2) = 3/20}}}
To get rid of the fractions we will multiply by the Lowest Common Denominator (LCD). The LCD here is: 20(4+x^2).
{{{20(4+x^2)(x/(4+x^2)) = 20(4+x^2)(3/20)}}}
Cancel common factors on each side:
{{{20*cross((4+x^2))(x/cross(4+x^2)) = cross(20)(4+x^2)(3/cross(20))}}}
leaving:
{{{20*x = (4+x^2)*3}}}
or
{{{20x = 12 + 3x^2}}}
Since this is a quadratic equation, we will get one side equal to zero:
{{{0 = 3x^2 - 20x + 12}}}
... then factor it (or use the quadratic formula):
{{{0 = (3x - 2)(x-6)}}}
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:
{{{3x-2 = 0}}} or {{{x-6 = 0}}}
Solving these we get:
{{{3x = 2}}} or {{{x = 6}}}
{{{x = 2/3}}} or {{{x = 6}}}<br>
Since the problem specifies integers, we must reject x = 2/3. So the only answer to the problem is x=6.