Find Where Undefined/Discontinuous (4x-3)/(x^2-9)-(2x-3)/(x-3)

$\frac{4 x - 3}{x^{2} - 9} - \frac{2 x - 3}{x - 3}$

Step 1

Set the denominator in $\frac{4 x - 3}{x^{2} - 9}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 9 = 0$

Step 2

Solve for $x$ .

Add $9$ to both sides of the equation.

$x^{2} = 9$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 3$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 3$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 3, - 3$

Step 3

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

$x - 3 = 0$

Step 4

Add $3$ to both sides of the equation.

$x = 3$

Step 5

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 $0$ .

$x = - 3, x = 3$

Step 6

Find Where Undefined/Discontinuous (4x-3)/(x^2-9)-(2x-3)/(x-3)

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