Adding and Subtracting Rational Expressions Explained

Why is it necessary to have a common denominator when adding or subtracting rational expressions?

• To simplify the expressions

• To make the numerators equal

• To ensure the denominators are the same

• To convert the expressions into whole numbers

In the example u - 6v / 16u^2 + u + 2v / 16u^2, what is the common denominator?

• 16

• u^2

• 16u^2

• 16u

What is the simplified form of the expression (u - 6v + u + 2v) / 16u^2?

• 2u - 4v / 16u^2

• u - 2v / 16u^2

• 2u - 4v / 8u^2

• u - 2v / 8u^2

When subtracting rational expressions, why is it important to put the numerator of the subtracted expression in parentheses?

• To factor the numerator

• To find the common denominator

• To simplify the expression

• To change the sign of each term inside

What is the least common denominator (LCD) of the expressions 7 / 3k^3 + 12k^2 and 3 / k + 4?

• 3k^2

• k^2(k + 4)

• 3k^2(k + 4)

• 3k^3

How do you simplify the expression 7x / (x + 1) - 3 / (x - 3)?

• Find the common denominator and subtract the numerators

• Factor the numerators

• Add the numerators directly

• Multiply the numerators and denominators

What is the simplified form of the expression (5x + 3) / (3(x - 1)) + (2x - 7) / (x^2 - 1)?

• 5x^2 + 14x - 18 / 3(x + 1)

• 5x^2 + 14x - 18 / (x + 1)(x - 1)

• 5x^2 + 14x - 18 / 3(x + 1)(x - 1)

• 5x^2 + 14x - 18 / 3(x - 1)

What is the simplified form of the expression -2x / (x + y) + 5x / (2(x + y))?

• x / (x + y)

• 1 / (x + y)

• x / 2

• 1 / 2

How do you handle rational expressions with opposite denominators, such as 3 / (4x - 5) + 9 / (5 - 4x)?

• Find the common denominator

• Multiply the numerators and denominators

• Factor out a negative one from one of the denominators

• Add the numerators directly

What is the simplified form of the expression (z + b) / (18z^2 + 12zb - 3zb - 2b^2) + (3z - b) / (36z^2 - b^2)?

• 15z^2 + 10zb - b^2 / (6z - b)

• 15z^2 + 10zb - b^2 / (3z + 2b)

• 15z^2 + 10zb - b^2 / (6z - b)(6z + b)(3z + 2b)

• 15z^2 + 10zb - b^2 / (6z - b)(6z + b)