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Rational Expressions

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**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

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**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.

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**All the x values in a given function.**

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

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

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**Simplifying Factor each expression completely List any restrictions**

Divide out any common factors Simplify and leave in factored form

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**Simplify the following rational expressions and state the domain**

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**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

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

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**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

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

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

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**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

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

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

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

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

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