Simplify Rational Expressions

Front

What is a rational expression?

Back

A rational expression is a fraction where both the numerator and the denominator are polynomials.

Front

How do you multiply rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together, then simplify if possible.

Front

What is the process for dividing rational expressions?

Back

To divide rational expressions, multiply by the reciprocal of the divisor and then simplify.

Front

What is the least common denominator (LCD) and why is it important?

Back

The least common denominator is the smallest expression that can be used as a common denominator for two or more rational expressions, important for adding or subtracting them.

Front

How do you add rational expressions with different denominators?

Back

To add rational expressions with different denominators, find the least common denominator, rewrite each expression with the LCD, and then combine the numerators.

Front

What is the significance of identifying values that make a rational expression undefined?

Back

Values that make the denominator zero render the rational expression undefined; these values must be excluded from the domain.

Front

How do you simplify a rational expression?

Back

To simplify a rational expression, factor both the numerator and the denominator and then cancel any common factors.

Front

What are the steps to factor a polynomial?

Back

To factor a polynomial, look for common factors, use techniques like grouping, or apply special factoring formulas (e.g., difference of squares).

Front

What is the difference between adding and multiplying rational expressions?

Back

Adding requires a common denominator, while multiplying involves multiplying numerators and denominators directly.

Front

What is a polynomial?

Back

A polynomial is an expression consisting of variables raised to non-negative integer powers and coefficients.