Find the Excluded Values (x^2-14x+49)/(6x^2-42x)

$\frac{x^{2} - 14 x + 49}{6 x^{2} - 42 x}$

Step 1

Set the denominator in $\frac{x^{2} - 14 x + 49}{6 x^{2} - 42 x}$ equal to $0$ to find where the expression is undefined.

$6 x^{2} - 42 x = 0$

Step 2

Solve for $x$ .

Factor $6 x$ out of $6 x^{2} - 42 x$ .

Factor $6 x$ out of $6 x^{2}$ .

$6 x (x) - 42 x = 0$

Factor $6 x$ out of $- 42 x$ .

$6 x (x) + 6 x (- 7) = 0$

Factor $6 x$ out of $6 x (x) + 6 x (- 7)$ .

$6 x (x - 7) = 0$

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

$x = 0$

$x - 7 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

The final solution is all the values that make $6 x (x - 7) = 0$ true.

$x = 0, 7$

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 $0$ .

$x = 0, x = 7$

Step 4

Find the Excluded Values (x^2-14x+49)/(6x^2-42x)

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