Problem 110 - Algebra and Trigonometry

Question

Explain how to find restrictions on the variable in a rational equation.

Step-by-Step Solution

Answer

The restriction on the variable in a rational equation is the value that makes the denominator equal to zero, thus making the expression undefined. In our example, the restriction is \(x \neq 2\).

Step 1: Identify the Denominator

In a rational equation, the denominator is the part of the equation located beneath the division line. It's important to correctly identify it because it's where our variable can lead to an undefined situation.

Step 2: Set the Denominator Equal to Zero

Once the denominator is identified, set up an equation where the denominator is equal to zero. For example, if the denominator is \(x-2\), we write this equation as \(x-2=0\).

Step 3: Solve the Equation

Our equation is now simple and resolvable. It's a matter of solving it for the variable. In our example, we solve \(x-2=0\) by adding 2 to both sides to get \(x=2\).

Step 4: Express the Restriction

Now that we know \(x=2\) makes the denominator zero, we have our restriction. The variable, \(x\), therefore cannot be equal to 2, because that would make the expression undefined. We then state: \(x \neq 2\), which means 'x cannot equal 2'.