Precalculus Examples

$\frac{3 a - 1}{a^{2} - b^{2}} - \frac{3 b - 1}{a^{2} - b^{2}}$

Step 1

Set the denominator in $\frac{3 a - 1}{a^{2} - b^{2}}$ equal to $0$ to find where the expression is undefined.

$a^{2} - b^{2} = 0$

Step 2

Solve for $a$ .

Tap for more steps...

Step 2.1

Add $b^{2}$ to both sides of the equation.

$a^{2} = b^{2}$

Step 2.2

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$| a | = | b |$

Step 2.3

Solve for $a$ .

Tap for more steps...

Step 2.3.1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$a = \pm | b |$

Step 2.3.2

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

Tap for more steps...

Step 2.3.2.1

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

$a = | b |$

Step 2.3.2.2

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

$a = - | b |$

Step 2.3.2.3

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

$a = | b |$

$a = - | b |$

$a = | b |$

$a = - | b |$

$a = | b |$

$a = - | b |$

$a = | b |$

$a = - | b |$

Step 3

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${a | a \in ℝ}$