x^2+6x-7/x^2+1 greater or equal to 2

We are asked to solve the inequality `(x^2+6x-7)/(x^2+1)>=2`

We can multiply both sides by x^2+1 since it is positive for all x:

`x^2+6x-7>=2(x^2+1)`

`x^2+6x-7>=2x^2+2 `

`x^2-6x+9<=0 `

`(x-3)^2<=0 `

Since the square of a real number is nonnegative, this is true only at x=3.

The solution is x=3.

The graph:

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Note that the graph approaches y=1 asymptotically"