Question 103892
{{{(3/(x-5)+1)/(1-(4/(x-5)))}}}
First lets go ahead and add each part;
{{{3/(x-5)+1}}}
we need common denominators to add, so we multiply x-5 to the second fraction ;
{{{3/(x-5)+(x-5)/(x-5)}}}
{{{(x-2)/(x-5)}}}=numerator
{{{1-(4/(x-5))}}}
We need common denominators;
{{{(x-5)/(x-5)-4/(x-5)}}}
{{{(x-9)/(x-5)}}}= denominator

Now our equation is;
{{{((x-2)/(x-5))/((x-9)/(x-5))}}}
When you divide fractions remember, you multiply the reciprocal;
{{{((x-2)/(x-5))*((x-5)/(x-9))}}}
Now cross cancel;
{{{((x-2)/cross(x-5))*(cross(x-5)/(x-9))}}}={{{(x-2)/(x-9)}}}
:)