Common Core: HSA-REI.A.2

Related Topics:

Algebra Word Problems

Common Core (Algebra)

Common Core for Mathematics

Examples, solutions, videos and lessons to help High School students learn how to solve
**simple rational** and radical equations in one
variable, and give examples showing how extraneous solutions may
arise.
### Suggested Learning Targets

**Extraneous Solutions to Rational Equations**

Examples:

Solve and eliminate any extraneous solutions:

x^{2}/(x + 2) = 4/(x + 2)

**Solve a Rational Equation with Extraneous Solution**

Solve a rational equation by multiplying both sides by the LCD and check the answers for extraneous solutions.

Solve 4(x - 3)/(x^{2} - 36) = 1/(6 - x) + 2x/(6 + x)

** Solving Rational Equations**

This video explains how to solve rational equations.

Examples:

1. 2/3 - 5/6 = 1/t

2. (x + 2)/(x - 6) = (x - 1)/(x + 2)

3. x/(x + 3) - x/(x - 2) = 10/(x^{2} + x - 6)

4. 4y/(y + 2) - 3y/(y - 1) = (y^{2} - 8y - 4)/(y^{2} + y - 2)
** Ex 1: Solving Rational Equations.**

Examples:

1. 2x/15 - 1/6 = x/5

2. 5/(x - 3) = 4/(x + 2)

**Ex 2: Solving Rational Equations.**

Examples:

1. 2/5x - 3 = 4/x

2. 2x - 16/x = 4

**Ex 3: Solving Rational Equations.**

Examples:

1. (x + 4)/x = 6/(x - 4)

2. 5/(x - 7) = -2x/(x + 3)

**Ex 4: Solving Rational Equations.**

Examples:

1. x/(x - 2) - x/(x^{2} - 4) = (x + 3)/(x + 2)

2. 5/(x - 3) = 4/(x + 2)

**Ex 5: Solving Rational Equations.**

Examples:

1. (x - 3)/(x + 6) + (x - 2)/(x - 3) = x^{2}/(x^{2} + 3x - 18)

2. 5/(x - 3) = 4/(x + 2)

**Applications of Rational Equations I**

The video explains application problems that use rational equations. Part 1 of 2.** Applications of Rational Equations II**

The video explains application problems that use rational equations. Part 2 of 2.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics:

Algebra Word Problems

Common Core (Algebra)

Common Core for Mathematics

- Solve simple rational and radical equations in one variable and provide examples of how extraneous solutions arise.

Examples:

Solve and eliminate any extraneous solutions:

x

Solve a rational equation by multiplying both sides by the LCD and check the answers for extraneous solutions.

Solve 4(x - 3)/(x

This video explains how to solve rational equations.

Examples:

1. 2/3 - 5/6 = 1/t

2. (x + 2)/(x - 6) = (x - 1)/(x + 2)

3. x/(x + 3) - x/(x - 2) = 10/(x

4. 4y/(y + 2) - 3y/(y - 1) = (y

Examples:

1. 2x/15 - 1/6 = x/5

2. 5/(x - 3) = 4/(x + 2)

Examples:

1. 2/5x - 3 = 4/x

2. 2x - 16/x = 4

Examples:

1. (x + 4)/x = 6/(x - 4)

2. 5/(x - 7) = -2x/(x + 3)

Examples:

1. x/(x - 2) - x/(x

2. 5/(x - 3) = 4/(x + 2)

Examples:

1. (x - 3)/(x + 6) + (x - 2)/(x - 3) = x

2. 5/(x - 3) = 4/(x + 2)

The video explains application problems that use rational equations. Part 1 of 2.

The video explains application problems that use rational equations. Part 2 of 2.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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