SOLUTION: Please Help Me Solve This Equation: {{{6/(x-1) = 4/(x-2) - 2/(x+1)}}} would the answer be no solution?

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Question 32803: Please Help Me Solve This Equation: 6%2F%28x-1%29+=+4%2F%28x-2%29+-+2%2F%28x%2B1%29 would the answer be no solution?
Found 2 solutions by longjonsilver, sarah_adam:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
multiply all terms by (x-1)(x+1)(x-2)
6%2F%28x-1%29+=+4%2F%28x-2%29+-+2%2F%28x%2B1%29+

+6%28x%2B1%29%28x-2%29+=+4%28x-1%29%28x%2B1%29+-+2%28x-1%29%28x-2%29+
+6%28x%5E2-x-2%29+=+4%28x%5E2-1%29+-+2%28x%5E2-3x%2B2%29+
+6x%5E2-6x-12+=+4x%5E2-4+-2x%5E2%2B6x-4+
+6x%5E2-6x-12+=+2x%5E2%2B6x-8+
+4x%5E2-12x-4+=+0+
+x%5E2-3x-1+=+0+

This does not factorise easily, so either complete the square or use the quadratic formula:

+x+=+%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29+
+x+=+%28-%28-3%29+%2B-+sqrt%28%28-3%29%5E2-4%281%29%28-1%29%29%29%2F%282%281%29%29+
+x+=+%283+%2B-+sqrt%289%2B4%29%29%2F%282%29+
+x+=+%283+%2B-+sqrt%2813%29%29%2F%282%29+

These are the 2 precise answers

jon.

Answer by sarah_adam(201) About Me  (Show Source):
You can put this solution on YOUR website!
6/(x-1) = 4(x+1) - 2(x-2)/ (x-2)(x+1)

6/(x-1) = 4x + 4- 2x - 4/(x-2)(x+1)

6/(x-1) = 4x-2x+4-4/ (x-2)(x+1) Hint (4x-2x = 2x; +4 – 4 = 0)

6/(x-1) = 2x/ (x-2)(x+1)

Now cross multiply:
6(x-2) (x+1) = 2x(x-1)
6(x^2 + x – 2x -2) = 2x^2 -2x
6(x^2 – x -2) =2(x^2 – x)
Now divide the entire equation with 2
6(x^2 – x -2)/2 = 2(x^2 – x)/2

3(x^2 – x -2) = (x^2 – x)
3x^2 – 3x – 6 = x^2 – x
Taking the like terms to same side:
3x^2 – 3x – 6 – x^2 + x = 0
3x^2 – x^2 -3x + x - 6 =0
2x^2 – 2x – 6 = 0
2(x^2 –x – 3) = 0
x^2 – x -3 =0
Solving the equation:
x = -b +sqrt(b^2+ 4*a*c)/2*a or x = -b - sqrt(b^2 - 4*a*c)/2*a
where a = coefficient of x^2
b = coefficient of x
c = constant
so here in this equation a = 1 ; b = -1 ; c = -3
Therfore
x = 1+ sqrt(1+12)/2 ==> x = 1+ sqrt(13)/2
or
x = 1- sqrt(1+12)/2 ==> x = 1-sqrt(13)/2