Question 78990
Does your problem look like this?


{{{((3/(x-5))-1)/(1-(4/(x-5)))}}}

In order to subtract fractions we need them to have a common denominator. So lets multiply both 1's by {{{(x-5)/(x-5)}}}

{{{((3/(x-5))-1((x-5)/(x-5)))/(1((x-5)/(x-5))-(4/(x-5)))}}}

So now we get this after multiplying


{{{((3/(x-5))-(x-5)/(x-5))/((x-5)/(x-5)-(4/(x-5)))}}}


Now we can combine the fractions


{{{((3-(x-5))/(x-5))/(((x-5)-4)/(x-5))}}}



Distribute the negative


{{{((3-x+5)/(x-5))/((x-5-4)/(x-5))}}}


Now combine like terms


{{{(((8-x))/(x-5))/((x-9)/(x-5))}}}


Now when we divide fractions, we multiply the first fraction, by the reciprocal of the 2nd


{{{(((8-x))/(x-5))*((x-5)/(x-9))}}}


Cancel like terms


{{{(((8-x))/cross((x-5)))*(cross((x-5))/(x-9))}}}

So our expression reduces to 


{{{(8-x)/(x-9)}}}