Find Where Undefined/Discontinuous y=(x-3)/(x^2-12x+27)

Solve Math

Algebra

$y = \frac{(x - 3)}{x^{2} - 12 x + 27}$

Set the denominator in $\frac{x - 3}{x^{2} - 12 x + 27}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 12 x + 27 = 0$

Solve for $x$ .

Tap for more steps...

Factor $x^{2} - 12 x + 27$ using the AC method.

Tap for more steps...

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 $27$ and whose sum is $- 12$ .

$- 9, - 3$

Write the factored form using these integers.

$(x - 9) (x - 3) = 0$

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

$x - 9 = 0$

$x - 3 = 0$

Set the first factor equal to $0$ and solve.

Tap for more steps...

Set the first factor equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Set the next factor equal to $0$ and solve.

Tap for more steps...

Set the next factor equal to $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

The final solution is all the values that make $(x - 9) (x - 3) = 0$ true.

$x = 9, 3$

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 $0$ .

$x = 3, x = 9$

Do you know how to Find Where Undefined/Discontinuous y=(x-3)/(x^2-12x+27)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.