Find Where Undefined/Discontinuous (x^2-3x-18)/(x^2-7x+6)

$\frac{x^{2} - 3 x - 18}{x^{2} - 7 x + 6}$

Step 1

Set the denominator in $\frac{x^{2} - 3 x - 18}{x^{2} - 7 x + 6}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 7 x + 6 = 0$

Step 2

Solve for $x$ .

Factor $x^{2} - 7 x + 6$ 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 $6$ and whose sum is $- 7$ .

$- 6, - 1$

Write the factored form using these integers.

$(x - 6) (x - 1) = 0$

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

$x - 6 = 0$

$x - 1 = 0$

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

The final solution is all the values that make $(x - 6) (x - 1) = 0$ true.

$x = 6, 1$

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 $0$ .

$x = 1, x = 6$

Step 4

Find Where Undefined/Discontinuous (x^2-3x-18)/(x^2-7x+6)

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