PLEASE EXPLAIN This is a college algebra problemThe answer i

PLEASE EXPLAIN. This is a college algebra problem.The answer is shown. Please explain or show work how to arrive at this answer.

20. What is the horizontal asymptote offx? 20-1) y 4 y 3

Solution

f(x)=[4x⁴+2x²]/(2(x-1)⁴)

horizontal asymptote y=lim_x-> f(x)

y=lim_x-> [4x⁴+2x²]/(2(x-1)⁴)

y=lim_x-> [x⁴(4+(2/x²))]/(2x⁴(1- (1/x))⁴)

y=lim_x-> [(4+(2/x²))]/(2(1- (1/x))⁴)

y= [(4+0)]/(2(1- 0)⁴)

y= 4/2

y=2

and

horizontal asymptote y=lim_x->- f(x)

y=lim_x->- [4x⁴+2x²]/(2(x-1)⁴)

y=lim_x->- [x⁴(4+(2/x²))]/(2x⁴(1- (1/x))⁴)

y=lim_x->- [(4+(2/x²))]/(2(1- (1/x))⁴)

y= [(4+0)]/(2(1- 0)⁴)

y= 4/2

y=2

y=2 is horizontal asymptote