Drag The Tiles To The Correct Boxes To Complete The Pairs.Match The Rational Expressions To Their Rewritten Forms.1. { \frac{x^2+4x-7}{x-1}$}$ 2. { \frac{2x^2-3x+7}{x-1}$}$ 3. { \frac{2x^2-x-7}{x-1}$}$ 4.
Introduction
Rational expressions are a fundamental concept in algebra, and simplifying them is a crucial skill to master. In this article, we will explore the process of simplifying rational expressions, with a focus on matching rational expressions to their rewritten forms. We will use the given examples to illustrate the steps involved in simplifying rational expressions.
What are Rational Expressions?
A rational expression is a fraction that contains variables and/or constants in the numerator and/or denominator. Rational expressions can be simplified by canceling out common factors between the numerator and denominator.
Simplifying Rational Expressions: A Step-by-Step Guide
To simplify a rational expression, we need to follow these steps:
- Factor the numerator and denominator: Factor the numerator and denominator of the rational expression to identify any common factors.
- Cancel out common factors: Cancel out any common factors between the numerator and denominator.
- Simplify the expression: Simplify the expression by combining any like terms.
Example 1: Simplifying a Rational Expression
Let's simplify the rational expression:
{\frac{x^2+4x-7}{x-1}$}$
To simplify this expression, we need to factor the numerator and denominator.
Factoring the Numerator and Denominator
The numerator can be factored as:
{x^2+4x-7 = (x+7)(x-1)$}$
The denominator is already factored as:
{x-1$}$
Canceling Out Common Factors
We can cancel out the common factor of {(x-1)$}$ between the numerator and denominator.
Simplifying the Expression
After canceling out the common factor, the simplified expression is:
{x+7$}$
Example 2: Simplifying a Rational Expression
Let's simplify the rational expression:
{\frac{2x^2-3x+7}{x-1}$}$
To simplify this expression, we need to factor the numerator and denominator.
Factoring the Numerator and Denominator
The numerator can be factored as:
${2x^2-3x+7 = (2x-7)(x-1)\$}
The denominator is already factored as:
{x-1$}$
Canceling Out Common Factors
We can cancel out the common factor of {(x-1)$}$ between the numerator and denominator.
Simplifying the Expression
After canceling out the common factor, the simplified expression is:
${2x-7\$}
Example 3: Simplifying a Rational Expression
Let's simplify the rational expression:
{\frac{2x^2-x-7}{x-1}$}$
To simplify this expression, we need to factor the numerator and denominator.
Factoring the Numerator and Denominator
The numerator can be factored as:
${2x^2-x-7 = (2x+7)(x-1)\$}
The denominator is already factored as:
{x-1$}$
Canceling Out Common Factors
We can cancel out the common factor of {(x-1)$}$ between the numerator and denominator.
Simplifying the Expression
After canceling out the common factor, the simplified expression is:
${2x+7\$}
Conclusion
Simplifying rational expressions is a crucial skill to master in algebra. By following the steps outlined in this article, you can simplify rational expressions and match them to their rewritten forms. Remember to factor the numerator and denominator, cancel out common factors, and simplify the expression. With practice, you will become proficient in simplifying rational expressions and solving problems involving rational expressions.
Discussion
Do you have any questions or comments about simplifying rational expressions? Share your thoughts and experiences in the discussion category below.
Matching Rational Expressions to Their Rewritten Forms
Now that we have simplified the rational expressions, let's match them to their rewritten forms.
| Rational Expression | Rewritten Form |
|---|---|
| {\frac{x^2+4x-7}{x-1}$}$ | {x+7$}$ |
| {\frac{2x^2-3x+7}{x-1}$}$ | ${2x-7\$} |
| {\frac{2x^2-x-7}{x-1}$}$ | ${2x+7\$} |
Match the rational expressions to their rewritten forms by dragging the tiles to the correct boxes.
Answer Key
| Rational Expression | Rewritten Form |
|---|---|
| {\frac{x^2+4x-7}{x-1}$}$ | {x+7$}$ |
| {\frac{2x^2-3x+7}{x-1}$}$ | ${2x-7\$} |
| {\frac{2x^2-x-7}{x-1}$}$ | ${2x+7\$} |
Introduction
In our previous article, we explored the process of simplifying rational expressions and matching them to their rewritten forms. In this article, we will answer some frequently asked questions about simplifying rational expressions.
Q: What is a rational expression?
A rational expression is a fraction that contains variables and/or constants in the numerator and/or denominator.
A: A rational expression is a fraction that contains variables and/or constants in the numerator and/or denominator.
Q: How do I simplify a rational expression?
To simplify a rational expression, you need to follow these steps:
- Factor the numerator and denominator: Factor the numerator and denominator of the rational expression to identify any common factors.
- Cancel out common factors: Cancel out any common factors between the numerator and denominator.
- Simplify the expression: Simplify the expression by combining any like terms.
Q: What is the difference between simplifying and canceling a rational expression?
Simplifying a rational expression involves factoring the numerator and denominator, canceling out common factors, and simplifying the expression. Canceling a rational expression involves canceling out common factors between the numerator and denominator, but not simplifying the expression.
Q: Can I simplify a rational expression with a variable in the denominator?
Yes, you can simplify a rational expression with a variable in the denominator. However, you need to be careful when canceling out common factors, as the variable may not be a common factor.
Q: How do I know if a rational expression can be simplified?
A rational expression can be simplified if it has a common factor between the numerator and denominator. If there are no common factors, the rational expression cannot be simplified.
Q: Can I simplify a rational expression with a negative exponent?
Yes, you can simplify a rational expression with a negative exponent. However, you need to be careful when canceling out common factors, as the negative exponent may not be a common factor.
Q: How do I simplify a rational expression with a fraction in the numerator or denominator?
To simplify a rational expression with a fraction in the numerator or denominator, you need to follow the same steps as simplifying a rational expression with a variable in the numerator or denominator.
Q: Can I simplify a rational expression with a radical in the numerator or denominator?
Yes, you can simplify a rational expression with a radical in the numerator or denominator. However, you need to be careful when canceling out common factors, as the radical may not be a common factor.
Q: How do I simplify a rational expression with a complex fraction?
To simplify a rational expression with a complex fraction, you need to follow the same steps as simplifying a rational expression with a variable in the numerator or denominator.
Conclusion
Simplifying rational expressions is a crucial skill to master in algebra. By following the steps outlined in this article, you can simplify rational expressions and answer frequently asked questions about simplifying rational expressions. Remember to factor the numerator and denominator, cancel out common factors, and simplify the expression. With practice, you will become proficient in simplifying rational expressions and solving problems involving rational expressions.
Discussion
Do you have any questions or comments about simplifying rational expressions? Share your thoughts and experiences in the discussion category below.
Additional Resources
For more information on simplifying rational expressions, check out the following resources:
I hope this article has been helpful in answering your questions about simplifying rational expressions. If you have any further questions or comments, please feel free to share them in the discussion category below.