Expert: Sherman D. - 4/23/2009

Question
[(6x)/(x+4])+(4)=(2x+2)/(x-1) The Answer is: -3/2 & 2       
Could you please show me how to arrive at these answers

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

multiply everything by (x + 4)(x - 1)

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

6x^2 - 6x + 4(x^2 - x + 4x - 4) = 2(x^2 + 4x + x + 4)

6x^2 - 6x + 4(x^2 + 3x - 4) = 2(x^2 + 5x + 4)

6x^2 - 6x + 4x^2 + 12x - 16 = 2x^2 + 10x + 8

10x^2 + 6x - 16 = 2x^2 + 10x + 8

8x^2 - 4x - 24 = 0

4(2x^2 - x - 6) = 0

2x^2 - x - 6 = 0

using the quadratic formula

x = (-b +/- sqrt(b^2 - 4ac))/(2a)

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

x = (1 +/- sqrt(1 + 48))/4
x = (1 +/- sqrt(49))/4
x = (1 +/- 7)/4
x = (8/4) or (-6/4)
x = 2 or (-3/2)