Question

What are the asymptotes and removable discontinuities, if any, of `f(x)=1/(8x+5)-x`?

Answer 1

Asymptote at `x=-5/8`

No removable discontinuities

Explanation:

You cannot cancel any factors in the denominator with factors in the numerator so there are no removable discontinuities (holes).

To solve for the asymptotes set the numerator equal to 0:

`8x+5=0`

`8x=-5`

`x=-5/8`

graph{1/(8x+5)-x [-10, 10, -5, 5]}