Find Where Undefined/Discontinuous (8/x+5/y)/(5x+8y)

$\frac{\frac{8}{x} + \frac{5}{y}}{5 x + 8 y}$

Step 1

Set the denominator in $\frac{8}{x}$ equal to $0$ to find where the expression is undefined.

$x = 0$

Step 2

Set the denominator in $\frac{5}{y}$ equal to $0$ to find where the expression is undefined.

$y = 0$

Step 3

Set the denominator in $\frac{\frac{8}{x} + \frac{5}{y}}{5 x + 8 y}$ equal to $0$ to find where the expression is undefined.

$5 x + 8 y = 0$

Step 4

Solve for $x$ .

Subtract $8 y$ from both sides of the equation.

$5 x = - 8 y$

Divide each term in $5 x = - 8 y$ by $5$ and simplify.

Divide each term in $5 x = - 8 y$ by $5$ .

$\frac{5 x}{5} = \frac{- 8 y}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 8 y}{5}$

Divide $x$ by $1$ .

$x = \frac{- 8 y}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{8 y}{5}$

Step 5

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

$- \frac{8 y}{5} \leq x \leq - \frac{8 y}{5}, x = 0$

$[0, 0] \cup [- \frac{8 y}{5}, - \frac{8 y}{5}]$

Step 6

Find Where Undefined/Discontinuous (8/x+5/y)/(5x+8y)

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