Find the range of `f(x)=(x^2+34 x-71)/(x^3+2x-7)`

Explanation

Let `(x^(2)+34x-71)/(x^(2)+2x-7)=y`

`impliesx^(2)(y-1)+(2y-34)x+71-7y=0`
For real values of `x` discriminant `ge0`
`:.(2y-34)^(2)-4(y-1)(71-7y)ge0`
`implies8y^(2)-112y+360ge0`
`impliesy^(2)-14h+45ge0`
`implies(y-9)(y-5)ge0`
`implies y epsilon (-oo,5]uu[9,oo)`
Hence `y` can never lie betwene 5 and 9.