Find all horizontal and vertical asymptotes if any If an ans

Find all horizontal and vertical asymptotes (if any). (If an answer does not exist, enter DNE.) s(x) = (2x - 1)(x + 9)/(5x - 1)(x - 8) vertical asymptote x = (smaller value) vertical asymptote x = (larger value) horizontal asymptote y =

Solution

vertical asymptotes

denominator =0

(5x-1)(x-8)=0

5x-1=0 , x-8 =0

5x =1 ,x=8

x=1/5 ,x=8

smaller value x =1/5

larger value x =8

horizontal asymptote :

y =lim_x->infinity [(2x-1)(x+9)]/[(5x-1)(x-8)]

y =lim_x->infinity [x²(2 -1/x)(1 +9/x)]/[x²(5 -1/x)(1 -8/x)]

y =lim_x->infinity [(2 -1/x)(1 +9/x)]/[(5 -1/x)(1 -8/x)]

y=[(2 -0)(1 +0)]/[(5 -0)(1 -0)]

y =2/5

horizontal asymptote y =2/5