Find Where Undefined/Discontinuous (y^2+5y-6)/(y^2-11y+10)

$\frac{y^{2} + 5 y - 6}{y^{2} - 11 y + 10}$

Step 1

Set the denominator in $\frac{y^{2} + 5 y - 6}{y^{2} - 11 y + 10}$ equal to $0$ to find where the expression is undefined.

$y^{2} - 11 y + 10 = 0$

Step 2

Solve for $y$ .

Factor $y^{2} - 11 y + 10$ 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 $- 11$ .

$- 10, - 1$

Write the factored form using these integers.

$(y - 10) (y - 1) = 0$

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

$y - 10 = 0$

$y - 1 = 0$

Set $y - 10$ equal to $0$ and solve for $y$ .

Set $y - 10$ equal to $0$ .

$y - 10 = 0$

Add $10$ to both sides of the equation.

$y = 10$

Set $y - 1$ equal to $0$ and solve for $y$ .

Set $y - 1$ equal to $0$ .

$y - 1 = 0$

Add $1$ to both sides of the equation.

$y = 1$

The final solution is all the values that make $(y - 10) (y - 1) = 0$ true.

$y = 10, 1$

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 $0$ .

$y = 1, y = 10$

Step 4

Find Where Undefined/Discontinuous (y^2+5y-6)/(y^2-11y+10)

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