Please help me!!Find an equation of the slant asymptote. Do not sketch the curve.? 1. y = (x^2 + 2) / (x + 2) 2. y = (4x^3 - 2x^2 + 1) / (2x^2 + x - 4) Solution let y = mx+c be the asymptote => y = mx+c, y = (x^2+2)/(x+2) should not have a solution for y =mx+c to be a asymptote => mx+c = (x^2+2)/(x+2) have no solution => (mx+c)(x+2) = x^2 +2 have no solution => m = 1 =>c = -2 => y = x-2 is the assymptotes 2) y = mx+c be an asymptote => y = mx+c, y = (4x^3-2x^2 +1)/(2x^2+x-4) should not have a solution for y =mx+c to be a asymptote => mx+c = (4x^3-2x^2 +1)/(2x^2+x-4) have no solution => (mx+c)(2x^2+x-4) = (4x^3 -2x^2+1) => m = 2, c = -2 => y = 2x-2 is the asymptote.

1. Please help me!!Find an equation of the slant asymptote. Do not sketch the curve.?
1. y = (x^2 + 2) / (x + 2)
2. y = (4x^3 - 2x^2 + 1) / (2x^2 + x - 4)
Solution
let y = mx+c be the asymptote
=>
y = mx+c, y = (x^2+2)/(x+2) should not have a solution for y =mx+c to be a asymptote
=>
mx+c = (x^2+2)/(x+2) have no solution
=>
(mx+c)(x+2) = x^2 +2 have no solution
=>
m = 1
=>c = -2
=>
y = x-2 is the assymptotes
2)
y = mx+c be an asymptote
=>
y = mx+c, y = (4x^3-2x^2 +1)/(2x^2+x-4) should not have a solution for y =mx+c to be a
asymptote
=>
mx+c = (4x^3-2x^2 +1)/(2x^2+x-4) have no solution
=>
(mx+c)(2x^2+x-4) = (4x^3 -2x^2+1)
=>
m = 2, c = -2
=>
y = 2x-2 is the asymptote