Simplifying and Operating with Rational Expressions

What is the result of simplifying the expression X^3 + X^2 over X + 1?

• X + 1

• X^3

• X^2 + 1

• X^2

How can X^2 - 1 over X^2 + 2X + 1 be simplified?

• X - 1 over X + 1

• X + 1 over X - 1

• X^2 - 1

• X^2 + 1

What is the result of multiplying (X + 2)/(X - 1) by (X^2 + 4X - 5)/(X + 3)?

• (X + 2)/(X + 3)

• (X - 1)/(X + 3)

• (X + 5)/(X + 3)

• (X - 1)/(X + 5)

What happens when you multiply a fraction by the reciprocal of another fraction?

• It results in subtraction

• It results in division

• It results in multiplication

• It results in addition

What is the result of dividing X + 3 over X - 4 by X^2 + X - 6 over X^2 - 3X - 4?

• X - 1 over X + 2

• X + 1 over X - 2

• X - 4 over X - 2

• X + 3 over X - 2

How do you find a common denominator for adding fractions with different denominators?

• Multiply each fraction by the denominator of the other over itself

• Subtract the denominators

• Add the denominators directly

• Multiply by the reciprocal of one fraction

What is the simplified form of the complex rational expression (1 + 1/X) / (1 - 1/X)?

• X + 1 over X - 1

• X - 1 over X + 1

• 1 over X

• X over 1

What is the correct way to simplify the expression 1 over root 2?

• Multiply by root 2 over root 2

• Add root 2 to the numerator

• Multiply by 2 over root 2

• Divide by root 2

What is the simplified form of the expression 1 over 1 - root 2?

• 1 - root 2

• -1 + root 2

• 1 + root 2

• -1 - root 2

How do you eliminate radicals from the denominator of a fraction?

• Multiply by the conjugate over itself if needed

• Add the radical to the numerator

• Subtract the radical from the denominator

• Multiply by the radical over itself