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

1 Answer

Answer:

#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#