Question

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

Answer 1

`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`