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

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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**

We have to solve 5x/(2x+2)=2x/(3x+3)+(2x+3)/(x+1) for x.

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

separate the (x+1) which is common as the denominator for all the terms

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

cancel (x+1)

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

multiply by 6

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

=> x = -18

**Therefore x = -18**

To solve the equation:5x/(2x+2)=2x/(3x+3)+(2x+3)/(x+1).

We factorise the denominators.

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

We mutiply both sides by 6(x+1):

5x*3 = 2x*2 +(2x+3)*6

15x = 4x+12x+18.

15x =16x +18.

0 = 16x+18-15x.

-18 = x.

Therefore x= -18.

First, we'll factorize the denominators:

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

We'll calculate LCD of the equation:

LCD = 2*3*(x+1)

LCD = 6(x+1)

We'll multiply by 6(x+1) both sides:

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

We'll simplify and we'll get:

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

We'll remove the brackets:

15x = 4x + 12x + 18

We'll move all terms that contain x to the left side:

-x = 18

We'll divide by -1:

**x = -18**

**The solution of the equation is x = -18.**