Trigonometry Examples

$\frac{20}{y} - \frac{8}{x} + \frac{3 x y}{x + y}$

Step 1

Find where the expression $0$ is undefined.

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Step 2

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

Step 3

$\frac{20 x^{2} + 12 y x + 3 x^{2} y^{2} - 8 y^{2}}{x y (x + y)} = 0$ is an equation of a line, which means there are no horizontal asymptotes.

No Horizontal Asymptotes

Step 4

Since there is no remainder from the polynomial division, there are no oblique asymptotes.

No Oblique Asymptotes

Step 5

This is the set of all asymptotes.

No Vertical Asymptotes

No Horizontal Asymptotes

No Oblique Asymptotes

Step 6