SOLUTION: Solve the equation 5x/2x+2 = 2x/3x+3 + 2x+3/x+1 First of all, is the LCD 6x +6? If it is, after I get done multiplying everything by 6x + 6, I get a huge problem that doesn't

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Solve the equation 5x/2x+2 = 2x/3x+3 + 2x+3/x+1 First of all, is the LCD 6x +6? If it is, after I get done multiplying everything by 6x + 6, I get a huge problem that doesn't       Log On


   

Question 29482: Solve the equation
5x/2x+2 = 2x/3x+3 + 2x+3/x+1
First of all, is the LCD 6x +6?
If it is, after I get done multiplying everything by 6x + 6, I get a huge problem that doesn't look like I can solve it.
This is what I get:
4x(squared)+ 4x +24x + 36 = 15x(squared) + 15x.
Is this even close?
Found 2 solutions by longjonsilver, askmemath:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+%285x%29%2F%282x%2B2%29+=+%282x%29%2F%283x%2B3%29+%2B+%282x%2B3%29%2F%28x%2B1%29+
ok, scale up all terms:

+%2815x%29%2F%286x%2B6%29+=+%284x%29%2F%286x%2B6%29+%2B+%2812x%2B18%29%2F%286x%2B6%29+
+%2815x%29+=+%284x%29+%2B+%2812x%2B18%29+
15x = 4x + 12x + 18
15x = 16x + 18
-x = 18
x = -18

Just so you can see that this is correct:
CHECK:
LHS:
+%285x%29%2F%282x%2B2%29+
+%285%29%28-18%29%29%2F%282%28-18%29%2B2%29+
+%28-90%29%29%2F%28-34%29+
45%2F17

RHS:
+%282x%29%2F%283x%2B3%29+%2B+%282x%2B3%29%2F%28x%2B1%29+
+%28%282%29%28-18%29%29%2F%283%28-18%29%2B3%29+%2B+%282%28-18%29%2B3%29%2F%28-18%2B1%29+
+%28-36%29%2F%28-51%29+%2B+%28-33%29%2F%28-17%29+
+%2836%2F51%29+%2B+%2833%2F17%29+
+45%2F17+

So, correct.

jon.

Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
5x/2x+2 = 2x/3x+3 + 2x+3/x+1
Consider only the denominators
2x+2 = 2(X+1)
3x+3 = 3(X+1)
x+1 = 1(x+1)
Since X+1 is common to all, you cancel them all out!!!
5x/2 = 2x/3 + 2x+3/1
you only have to worry abt 1,2,3 whose LCM becomes 6
So basically your LCD is 6
can you solve from here?