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
2 Answers
jeew-m | College Teacher | (Level 1) Educator Emeritus
`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.
crmhaske | College Teacher | (Level 3) Associate Educator
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