Find Where Undefined/Discontinuous (y-8)/(y^2-3y-10)

$\frac{y - 8}{y^{2} - 3 y - 10}$

Step 1

Set the denominator in $\frac{y - 8}{y^{2} - 3 y - 10}$ equal to $0$ to find where the expression is undefined.

$y^{2} - 3 y - 10 = 0$

Step 2

Solve for $y$ .

Factor $y^{2} - 3 y - 10$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Write the factored form using these integers.

$(y - 5) (y + 2) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y - 5 = 0$

$y + 2 = 0$

Set $y - 5$ equal to $0$ and solve for $y$ .

Set $y - 5$ equal to $0$ .

$y - 5 = 0$

Add $5$ to both sides of the equation.

$y = 5$

Set $y + 2$ equal to $0$ and solve for $y$ .

Set $y + 2$ equal to $0$ .

$y + 2 = 0$

Subtract $2$ from both sides of the equation.

$y = - 2$

The final solution is all the values that make $(y - 5) (y + 2) = 0$ true.

$y = 5, - 2$

Step 3

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 $0$ .

$y = - 2, y = 5$

Step 4

Find Where Undefined/Discontinuous (y-8)/(y^2-3y-10)

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