R.5 Rational Expressions

Question 1

Rational expression

Answer 1

An expression that can be written as a quotient of two polynomials.

Question 2

What is another word for rational expression?

Answer 2

Algebraic expression

Question 3

What is simplest form?

Answer 3

A rational expression is in simplest form when the numerator and denominator have no common factors.

Question 4

Fundamental property of rational expressions

Answer 4

If P, Q, and R are polynomials, and Q, R != 0:

(P * R / Q * R) = (P / Q)

(P / Q) = (P * R / Q * R)

An expression can be simplified by canceling common factors in the numerator and denominator.

An equivalent expression can be formed by multiplying the numerator an denominator by the same nonzero polynomial.

Question 5

What does (a - b) / (b - a) simplify to?

Answer 5

-1

Question 6

How are rational expressions multiplied?

Answer 6

Given that P, Q, R, and S are polynomials with Q, R, and S != 0.

(P / Q) * (R / S) = (PR / QS)

1) Factor all numerators and denominators fully.
2) Reduce common factors.
3) Multiply Numerator by Numerator and Denominator by Denominator

Question 7

How are rational expressions divided?

Answer 7

Given that P, Q, R and S are polynomials with Q, R, and S != 0.

(P / Q) / (R / S) = (P / Q) * (S / R) = (PS / QR)

Question 8

What is a synonym for simplest form?

Answer 8

lowest terms

Question 9

How do you add or subtract rational expressions?

Answer 9

1) Find the lowest common denominator of all rational expressions.
2) Build equivalent expressions using the LCD.
3) Add or subtract numerators as indicated.
4) Write the result in lowest terms.

Question 10

What is a compound fraction?

Answer 10

Rational expressions whose numerator or denominator contain a fraction.

Question 11

What is the first method of simplifying compound fractions.

Answer 11

1) add/subtract fractions in the numerator, writing them a a single expression.
2) Add/subtract expressions in the denominator, also writing them as a single expression.
3) Multiply the numerator by the reciprocal of the denominator and simplify if possible.

Question 12

What is the second method of simplifying compound fractions?

Answer 12

1) Find the LCD of all fractions in the numerator and denominator.
2) Multiply the numerator and denominator by this LCD and simplify.
3) Simplify further if possible.