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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation to be solved is: 5x/(2x+2) = 2x/(3x+3)+(2x+3)/(x+1)

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

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

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

=> 5x/2 = (2x + 6x + 9)/3

=> 15x = 16x + 18

=> x = -18

The solution to the equation is x = -18

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

We'll compute 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 requested solution of the equation is x = -18.

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