Find the Excluded Values ((x^2-3x-10)/(x-3))/((x+2)/(3x-9))

$\frac{\frac{x^{2} - 3 x - 10}{x - 3}}{\frac{x + 2}{3 x - 9}}$

Step 1

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

$x - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

$x = 3$

Step 3

Set the denominator in $\frac{x + 2}{3 x - 9}$ equal to $0$ to find where the expression is undefined.

$3 x - 9 = 0$

Step 4

Solve for $x$ .

Add $9$ to both sides of the equation.

$3 x = 9$

Divide each term in $3 x = 9$ by $3$ and simplify.

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x = 3$

Step 5

Set the denominator in $\frac{\frac{x^{2} - 3 x - 10}{x - 3}}{\frac{x + 2}{3 x - 9}}$ equal to $0$ to find where the expression is undefined.

$\frac{x + 2}{3 x - 9} = 0$

Step 6

Solve for $x$ .

Set the numerator equal to zero.

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 7

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 $0$ .

$x = - 2, x = 3$

Step 8

Find the Excluded Values ((x^2-3x-10)/(x-3))/((x+2)/(3x-9))

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