Find Where Undefined/Discontinuous (x-3)/((x+5)(x-7))

$\frac{x - 3}{(x + 5) (x - 7)}$

Step 1

Set the denominator in $\frac{x - 3}{(x + 5) (x - 7)}$ equal to $0$ to find where the expression is undefined.

$(x + 5) (x - 7) = 0$

Step 2

Solve for $x$ .

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

$x + 5 = 0$

$x - 7 = 0$

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

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 $(x + 5) (x - 7) = 0$ true.

$x = - 5, 7$

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 $0$ .

$x = - 5, x = 7$

Step 4

Find Where Undefined/Discontinuous (x-3)/((x+5)(x-7))

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