Rational Expressions.

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Presentation transcript:

Rational Expressions

Rational Expression Examples An 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 The denominator cannot equal zero. The restrictions indicate when the denominator equals zero. Factor the denominator completely and set each factor not equal to zero. Solve for the given variable.

All the x values in a given function. Domain of A Function All the x values in a given function.

State the restrictions on the domain and state the domain of the function.

Simplifying Factor each expression completely List any restrictions Divide out any common factors Simplify and leave in factored form

Simplify the following rational expressions and state the domain

Multiplying and Dividing Change division to multiplication of the inverse Factor each expression completely Divide out any common factors Simplify and leave in factored form

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

Adding and Subtracting Factor each denominator completely Find the LCM of the denominators Multiply each term by the LCM Simplify the numerator The denominator is the LCM Simplify and leave in factored form

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

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

Complex Rational Factor each denominator completely Find the LCM Multiply numerator / denominator by the LCM Combine all like terms Simplify and leave in factored form

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

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

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

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