Question 83702
Here goes:

(x/(2x+2))=((-2x)/(4x+4))+((2x+3)/(x+1))

step 1:
Simplify:
(x/(2(x+1)))=((-2x)/(4(x+1)))+((2x+3)/(x+1))

Step 2:
Cancel like terms:
(x/(2(x+1)))=((-x)/(2(x+1)))+((2x+3)/(x+1))

step 3: 
greatest common denominator-multiply last quotient by 2 to make GCD.
(x/(2(x+1)))=((-x)/(2(x+1)))+((4x+6)/(2(x+1))

step 4:
gather all quotients on one side of equal signs:
0=((-x)/(2(x+1)))+((4x+6)/(2(x+1))-((x)/(2(x+1)))

step 5: 
Simplify:
(-x+(4x+6)-x)/(2(x+1))

step 6:
Solve
(2x+6)/(2(x+1)

step 7:
Simplify:
(2(x+3))/(2(x+1))

Step 8:
Cancel 2s to get your final answer of:
(x+3)/(x+1)