Describe and corect the error. 3/x + 6/x+3 = 8/x+1 LCD = x(x + 3)(x + 1) 3(x + 3)(x + 1) + 6x(x + 1) = 8 3(x^2 + 4x + 3) + 6x^2 + 6x = 8 3x^2 + 12x + 9 + 6x^2 + 6x = 8 9x^2 + 18x + 1 = 0 x = -18 +-...
Describe and corect the error.
3/x + 6/x+3 = 8/x+1
LCD = x(x + 3)(x + 1)
3(x + 3)(x + 1) + 6x(x + 1) = 8
3(x^2 + 4x + 3) + 6x^2 + 6x = 8
3x^2 + 12x + 9 + 6x^2 + 6x = 8
9x^2 + 18x + 1 = 0
x = -18 +- sqrt(18^2 - 4(9)(1))/2(9)
x = sqrt(-18 +- sqrt(288))/18
x = -18 +- 12 sqrt(2)/18
x = -3 +- 2 sqrt(2)/3
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`3/x + 6/(x+3) = 8/(x+1)`
For denominator we have three terms x,(x+3) and (x+1). If we can remove these terms the calculation will become easy.
So we have to multiply both sides of the expression by x(x+3)(x+1).
`3/x + 6/x+3 = 8/x+1`
`x(x+3)(x+1) (3/x + 6/(x+3)) = (8/(x+1))x(x+3)(x+1)`
`3(x+3)(x+1)+6(x)(x+1) = 8(x)(x+3)`
`3(x^2+4x+3)+6(x^2+x) = 8(x^2+3x)`
`9x^2+18x+9 = 8x^2+24x`
`x^2-6x+9 = 0`
`(x-3)^2 = 0`
`x-3 = 0`
`x = 3`
So the answer is x = 3
Note
RHS of your after appyling LCD is wrong.

The error occurs in the third step. The third term, the term to the right of the equal sign, is missing x(x+3):
`3/x+6/(x+3)=8/(x+1)`
`(3(x+3)(x+1))/(x(x+1)(x+3))+(6x(x+1))/(x(x+1)(x+3))=(8x(x+3))/(x(x+1)(x+3))`
`3(x^2+4x+3)+6x^2+6x-8x^2-24x=0`
`x^2-6x+9=0`
Using factoring:
`(x-3)(x-3)=0`
Therefore, there is one solution x=3