Adding and Subtracting Rational Expressions

What is the key idea when simplifying a fraction with a radical in the denominator?

• Subtracting the numerator from the denominator

• Adding the numerator and the denominator

• Rationalizing the denominator

• Multiplying the numerator by the denominator

When rationalizing a denominator with a single term, what do you multiply the numerator and denominator by?

• The reciprocal of the numerator

• The reciprocal of the denominator

• The square root of the numerator

• The square root of the denominator

In the example 4 - √3 / √3, what is the result after rationalizing the denominator?

• 4√3 - 3 / √3

• 4√3 - 3 / 3

• 4√3 - 3 / 9

• 4 - 3 / 3

In the example 5 + √3 / √18, why is it beneficial to multiply by √2 instead of √18?

• To create a perfect square in the denominator

• To simplify the numerator

• To make the fraction improper

• To eliminate the numerator

What is the result of rationalizing the denominator in the example 5 + √3 / √18?

• 5 + √3 / 6

• 5 + √6 / 6

• 5√2 + √6 / 6

• 5√2 + √3 / 6

What is a conjugate in the context of rationalizing denominators?

• A term with the same sign in the middle

• A term with the opposite sign in the middle

• A term with the same terms but different coefficients

• A term with the opposite terms but same coefficients

What is the conjugate of 3 + √5?

• 3 + √5

• 5 - √3

• 3 - √5

• √5 - 3

When rationalizing a binomial denominator, what is the first step?

• Subtract the numerator from the denominator

• Multiply by the reciprocal of the numerator

• Multiply by the conjugate of the denominator

• Add the numerator and the denominator

In the example 3 - √3 / 3 + √3, what is the result after rationalizing the denominator?

• 3 + 3√3 / 6

• 3 - √3 / 6

• 3 - 3√3 / 6

• 3 + √3 / 6

How do you find the width of a rectangle if the area is 14 + 7√2 and the length is 4 + √2?

• Subtract the length from the area and rationalize the denominator

• Add the length to the area and rationalize the denominator

• Divide the area by the length and rationalize the denominator

• Multiply the area by the length and rationalize the denominator