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## Algebra 2

### Course: Algebra 2>Unit 10

Lesson 6: Solving equations by graphing

# Equations: FAQ

## What are rational equations?

Rational equations are equations that contain one or more fractions. To solve them, we usually try to get rid of the fractions, and then solve the equation with other strategies we know.
Here are a few examples of different rational equations:
• start fraction, 2, x, plus, 1, divided by, x, minus, 3, end fraction, equals, 2
• start fraction, x, divided by, 2, end fraction, plus, start fraction, 1, divided by, 3, end fraction, equals, start fraction, 5, divided by, 6, end fraction
• start fraction, 3, x, plus, 2, divided by, x, squared, minus, 1, end fraction, equals, start fraction, 2, x, divided by, x, squared, plus, 3, end fraction

## What are square-root equations?

Square-root equations are equations that contain square roots. To solve them, we usually isolate the square root on one side of the equation, and square both sides in order to get rid of the square root.
Here are a few examples of different square-root equations:
• square root of, x, end square root, plus, 2, equals, 6
• square root of, 2, x, plus, 1, end square root, equals, 9
• left parenthesis, square root of, x, end square root, right parenthesis, squared, equals, 64

## What are extraneous solutions?

Sometimes when we solve an equation, we'll find a solution that makes one side of the equation equal to the other, but doesn't actually work when we plug it back into the original equation. This is called an extraneous solution. It's really important to always check our solutions by substituting them back into the original equation, to make sure they're not extraneous.

## What are cube-root equations?

Cube-root equations are equations that contain cube roots. To solve them, we usually isolate the cube root on one side of the equation, and cube both sides in order to get rid of the cube root.