Simplifying Rational Expressions

The video tutorial covers simplifying rational expressions by factoring, using exponent rules, and eliminating common factors. It explains the product, quotient, power, and reciprocal rules for exponents. The tutorial provides examples to demonstrate different methods of simplification, including handling negative exponents and factoring trinomials. The use of a polynomial root finder is also shown to aid in factoring. The video concludes with a comprehensive example of factoring out common factors and simplifying the expression.

What is the first step in simplifying rational expressions?

• Write the final expression

• Simplify the coefficients

• Factor everything possible

• Eliminate exponents

When multiplying variables with exponents, what should you do with the exponents?

• Subtract them

• Add them

• Divide them

• Multiply them

What is the result of dividing x^3 by x^2 using exponent rules?

• x^5

• x^1

• x^6

• 1/x

How do you handle a negative exponent, such as x^-3?

• Flip it to the denominator

• Convert it to a positive in the numerator

• Multiply by -1

• Ignore the negative sign

In the expression 12y/y^3, what is the simplified form using exponent rules?

• 12y^3

• 12/y^2

• y^2/12

• 12y^2

What is the simplified form of 16/36 when factoring out the greatest common divisor?

• 2/7

• 4/9

• 1/2

• 8/18

How do you simplify the expression x^3/x^5?

• 1/x^2

• x^8

• x^2

• x^-2

What does the polynomial root finder tool help with in simplifying expressions?

• Solving equations

• Factoring polynomials

• Determining coefficients

• Finding the highest exponent

What is the result of simplifying the expression (y + 8)/(y^2 + 2y - 48) after factoring?

• y + 8

• (y - 6)/(y + 8)

• 1/(y - 6)

• 1

After factoring out common terms, what is left in the expression 12a^3 + 3a over 12a^3 + 6a^2?

• a - 1

• 2a - 1

• 2a + 1

• 3a + 1