Solve the equation x+3/(x-2)+x-4=7/(x-2)?

1 Answer
Oct 20, 2016

x=2+-sqrt2

Explanation:

x+3/(x-2)+x-4=7/(x-2)
Multiply by (x-2)
x(x-2)+3+(x-4)(x-2)=7
Developing, we get
x^2-2x+3+x^2-6x+8-7=0
2x^2-8x+4=0
Dividing by 2
x^2-4x+2=0
Delta=(-4)^2-4*1*2=16-8=8
So the solution is x=(4+-sqrt8)/2=(4+-2sqrt2)/2=2+-sqrt2