Question 198575
{{{(5/(3r-1)-5)/(5/(3r-1)+5)}}} Start with the given expression.



{{{((5/cross((3r-1)))cross((3r-1))-5(3r-1))/((5/cross((3r-1)))cross((3r-1))+5(3r-1))}}} Multiply EVERY term by the inner LCD {{{3r-1}}} to clear out the inner fractions.



{{{(5-5(3r-1))/(5+5(3r-1))}}} Simplify



{{{(5-15r+5)/(5+15r-5)}}} Distribute



{{{(10-15r)/(15r)}}} Combine like terms.



{{{(5(2-3r))/(15r)}}} Factor the numerator



{{{(5(2-3r))/(5*3r)}}} Factor the denominator



{{{(cross(5)(2-3r))/(cross(5)*3r)}}} Cancel out the common terms.



{{{(2-3r)/(3r)}}} Simplify



So {{{(5/(3r-1)-5)/(5/(3r-1)+5)=(2-3r)/(3r)}}}