rational expressions. rational expression an expression that can be written in the form p/q, where p...

Rational Expressions

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Rational Expressions

Rational ExpressionAn expression that can be

written in the form P/Q, where P and Q are polynomials and Q

is not equal to zero.Examples

Restrictions on Variables

1.The denominator cannot equal zero.

2.The restrictions indicate when the denominator equals zero.

3.Factor the denominator completely and set each factor not equal to zero.

4.Solve for the given variable.

Page 4: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Domain of A FunctionAll the x values in a given

function.

Page 5: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

State the restrictions on the domain and state the domain

of the function.

Page 6: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Simplifying1.Factor each expression

completely

2.List any restrictions

3.Divide out any common factors

4.Simplify and leave in factored form

Page 7: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Simplify the following rational expressions and state the

domain

Page 8: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Multiplying and Dividing1.Change division to

multiplication of the inverse

2.Factor each expression completely

3.Divide out any common factors

4.Simplify and leave in factored form

Page 9: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Perform the indicated operation and leave your answer in factored form.

Page 10: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Adding and Subtracting1.Factor each denominator

completely

2.Find the LCM of the denominators

3.Multiply each term by the LCM

4.Simplify the numerator

5.The denominator is the LCM

6.Simplify and leave in factored form

Page 11: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Perform the indicated operation and leave your answer in factored form.

Page 12: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Perform the indicated operation and leave your answer in factored form.

Page 13: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Complex Rational1.Factor each denominator

completely

2.Find the LCM

3.Multiply numerator / denominator by the LCM

4.Combine all like terms

5.Simplify and leave in factored form

Page 14: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Perform the indicated operation and leave your answer in

factored form.

Page 15: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Perform the indicated operation and leave your answer in

factored form.

Page 16: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Perform the indicated operation and leave your answer in

factored form.

Page 17: Rational Expressions. Rational Expression An expression that can be written in the form P/Q, where P and Q are polynomials and Q is not equal to zero

Perform the indicated operation and leave your answer in

factored form.

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