Simplifying Rational Expressions

TL;DR

Learn how to simplify rational expressions by factoring, canceling common factors, and reducing terms.

Transcript

in this lesson we're going to focus on simplifying rational expressions so let's start with our first example 35 x to the fifth over 49 x squared go ahead and simplify this expression we can reduce 35 and 49 by seven 35 divided by seven is five 49 divided by 7 is 7. now whenever you're dividing by a common base you're allowed to subtract the expone... Read More

Key Insights

• 😑 Rational expressions can be simplified by factoring and canceling out common factors.
• 😑 The difference of squares technique is useful for factoring expressions of the form x² - a².
• 🍉 Trinomials with a leading coefficient of one can be factored by finding two numbers that multiply to the constant term and add to the middle term.

Questions & Answers

Q: How do you simplify rational expressions?

To simplify rational expressions, you need to factor the numerator and denominator, cancel out common factors, and reduce the terms.

Q: What is the difference of squares technique?

The difference of squares technique is used to factor expressions like x² - 16. It involves taking the square root of each term and changing the sign of the second term.

Q: How do you factor trinomials with a leading coefficient of one?

To factor trinomials with a leading coefficient of one, find two numbers that multiply to the constant term and add to the middle term. Use these numbers to rewrite the middle term in the factored form.

Q: Why is it important to factor completely in rational expressions?

Factoring completely allows you to cancel out common terms and simplify the rational expression. It helps to eliminate unnecessary factors and reduce the expression to its simplest form.

Summary & Key Takeaways

• To simplify a rational expression, find the greatest common factor (GCF) of the terms on top and bottom and cancel it out.

• Use the difference of squares technique to factor expressions like x² - 16 into (x + 4)(x - 4).

• For trinomials with a leading coefficient of one, find two numbers that multiply to the constant term and add to the middle term to factor them completely.

• Factor completely to cancel out common terms and simplify the rational expression.