Question

What is the horizontal asymptote of `y=((2x+3)(5x-2))/(7x^2-3)` ?

Answer 1

Its horizontal asymptote is `y=10/7`.

By taking the limits at infinity,
`lim_{x to infty}{(2x+3)(5x-2)}/{7x^2-3}`
by divide the numerator and the denominator by `x^2`,
`=lim_{x to +infty}{(2+3/x)(5-2/x)}/{7-3/x^2}={(2+0)(5-0)}/{7-0}=10/7`

Similarly, you can find
`lim_{x to -infty}{(2x+3)(5x-2)}/{7x^2-3}=10/7`

Hence, there is only one horizontal asymptote `y=10/7`.