Solve the equation 5x/(2x+2)=2x/(3x+3)+(2x+3)/(x+1)

Given the equation 5x/ (2x+2) = 2x/(3x+3)  +
(2x+3)/(x+1).

We need to find x values that satisfies the
equation.

First, we need to determine the common
denominator.

Let us factor all
denominators. 

==> 5x/ 2(x+1) = 2x/3(x+1)  +
(2x+3)/(x+1)

Then, we conclude that the common denominator
is 6(x+1).

==> 3*5x/ 6(x+1) = 3*2x/6(x+1)  +
6(2x+3)/ 6(x+1)

==> 15x/6(x+1) = 6x/6(x+1) +
6(2x+3)/6(x+1).

Now we will reduce the
denominator.

==> 15x = 4x +
6(2x+3)

==> 15x = 4x + 12x +
18

==> 15x - 4x - 12x =
18

==> x=
-18