# 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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### 2 Answers

`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