Describe and correct the error 11 3x 6x 3 8x 1 LCD x x

Describe and correct the error. 11. 3/x + 6/x + 3 = 8/x + 1 LCD = x (x + 3) (x + 1) 3 (x + 3) (x + 1) + 6x (x + 1) 3 (x^2 + 4x + 3) + 6x^2 + 6x = 8 3x^2 + 12x + 9 + 6x^2 + 6x = 8 9x^2 + 18x + 1 = 0 x = -18 plusminus squareroot 18^2 - 4 (9) (1)/2 (9) = squareroot -18 plusminus squareroot 288/18 = -18 plusminus 12 squareroot 2/18 x = -3 plusminus 2 squareroot 2/3 r^2 - 7r + 12/r + 4 + r^2 - 7r + 12/r^2 + 6r + 8 = (r - 3) (r - 4)/r + 4 + (r - 4) (r - 3)/(r + 2) (r + 4) = r + 4/(r - 3) (r - 4) middot (r - 4) (r - 3)/(r + 2) (r + 4) = 1/r + 2

Solution

3/x + 6/(x+3) = 8/(x+1)

LCD as x(x+1)(x+3)

Multiplying both sides with x(x+1)(x+3)

we get 3(x+1)(x+3) + 6(x+1)x = 8x(x+3)   < ------ mistake on RHS

9x^2 + 18x + 9 = 8x^2 + 24x

9x^2 - 6x +9 =0

3x^2 - 2x + 3=0

x= ( 2 +/- sqrt(4 - 36))/6 = 1/3 +/- (2sqrt2/3)i