+386
I need to find the ensemble of solutions for the equality that follows:
3 - ( x/ (x-3) ) = 2 x / (x+6)
Sorry Tony!. I only have ONE solution for you!.
Solve for x:
x/(x - 3) = (2 x)/(x + 6)
Cross multiply:
x (x + 6) = 2 x (x - 3)
Expand out terms of the left hand side:
x^2 + 6 x = 2 x (x - 3)
Expand out terms of the right hand side:
x^2 + 6 x = 2 x^2 - 6 x
Subtract 2 x^2 - 6 x from both sides:
12 x - x^2 = 0
Factor x and constant terms from the left hand side:
-(x (x - 12)) = 0
Multiply both sides by -1:
x (x - 12) = 0
Split into two equations:
x - 12 = 0 or x = 0
Add 12 to both sides:
Answer: |x = 12 or x = 0
+33653 Hmm. Guest #1 seems to have forgotten the initial 3.
3 - x/(x-3) = 2x/(x+6)
Multiply by (x-3)(x+6):
3(x-3)(x+6) -x(x+6) = 2x(x-3)
3(x^2 + 3x - 18) - x^2 - 6x = 2x^2 - 6x
2x^2 + 3x - 54 = 2x^2 - 6x
9x = 54
x = 6
.
+386 So there could be only one answer right?
In my exercices it says "find the ensemble of solutions ("S") of these equations"....
