Question 118989
You don't say what you want to do with this expression.  Please be more specific in the future about what you are asked to do in the problem.  


{{{((3x+1)/( 2x-6))  - (( x+2) /( x-3))}}}


Presuming that you only have to add the fractions and simplify:


Step 1:  Find the LCD.


{{{2x-6=2(x-3)}}} so {{{2x-6}}} and {{{x-3}}} have a common factor of {{{x-3}}}.  Therefore your LCD is {{{2x-6}}}


Step 2:  Apply the LCD.


{{{((3x+1)/( 2x-6))  - (2( x+2) /( 2x-6))}}}


Step 3:  Apply the distributive property to the 2nd fraction's numerator


{{{((3x+1)/( 2x-6))  +(-2x-4) /( 2x-6))}}}


Step 4:  Add the numerators


{{{((3x+1)+(-2x-4))/( 2x-6)}}}


Step 5:  Collect like terms


{{{(x-3)/(2x-6)}}}


Step 6:  Factor the denominator


{{{(x-3)/2(x-3)}}}


Step 7:  Divide {{{x-3}}} by {{{x-3}}}


{{{cross(x-3)/(2*cross(x-3))=1/2}}}