Question 537909
{{{f(x) = (2x^2-10x)/(4x^2-100)}}} Factor an x from the numerator.
{{{f(x) = x(2x-10)/(4x^2-100)}}} The denominator is the difference of squares and can be factored: {{{A^2-B^2 = (A-B)(A+B)}}}.
{{{f(x) = x*cross((2x-10))/cross((2x-10))(2x+10)}}} = {{{highlight(x/(2x+10))}}}
Notice that if you were to substitute {{{x = -5}}} in the denominator of the simplified solution, you would have division by zero, which is a no-no in math. Also note that if you were to substitute {{{x = 5}}} or {{{x = -5}}} in the denominator of the given function, you would have division by zero, so {{{x = 5}}} and {{{x = -5}}} are not allowed.
The domain (all allowable values of x) is all real numbers except 5 and -5.