How do we simplify rational expressions

The video tutorial covers simplifying rational expressions, starting with basic fraction reduction and moving to more complex rational expressions involving polynomials. It explains the use of properties of exponents and division to simplify expressions. The tutorial emphasizes the importance of rewriting expressions to apply division properties effectively, often requiring factoring. The goal is to achieve the most simplified form of rational expressions.

What is the first step in simplifying a fraction where the numerator is larger than the denominator?

• Multiply both the numerator and the denominator by the same number.

• Add the numerator and the denominator.

• Subtract the denominator from the numerator.

• Divide both the numerator and the denominator by their greatest common divisor.

When simplifying the expression 3x/15x, what is the result?

• 5/x

• x/5

• 1/5

• 3/15

How do you simplify the expression 3x^2/15x using properties of exponents?

• Multiply the exponents.

• Add the exponents.

• Subtract the exponents.

• Divide the exponents.

What is the purpose of factoring in simplifying complex rational expressions?

• To increase the number of terms.

• To rewrite expressions as a product for easier simplification.

• To convert expressions into fractions.

• To eliminate all variables.

In the expression (3x + 1)/(15x + 1), what allows the expression to be simplified?

• The exponents are equal.

• The expressions in the numerator and denominator are identical.

• The coefficients are the same.

• The terms are all constants.