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

What does it mean to simplify a rational expression?

Back

To simplify a rational expression means to reduce it to its simplest form, where the numerator and denominator have no common factors other than 1.

Front

How do you factor a polynomial?

Back

To factor a polynomial, you look for common factors, use techniques like grouping, or apply special formulas such as the difference of squares.

Front

What is the difference of squares formula?

Back

The difference of squares formula states that a^2 - b^2 = (a - b)(a + b).

Front

What is the first step in simplifying a rational expression?

Back

The first step is to factor both the numerator and the denominator completely.

Front

How do you identify common factors in a rational expression?

Back

Common factors can be identified by factoring both the numerator and denominator and looking for identical factors.

Front

What happens to a rational expression when you cancel common factors?

Back

When you cancel common factors, you simplify the expression, making it easier to work with.

Front

What is the importance of identifying restrictions in rational expressions?

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Identifying restrictions is important because it shows the values that make the denominator zero, which are not allowed in the expression.

Front

What is a polynomial?

Back

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

Front

What is the standard form of a polynomial?

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The standard form of a polynomial is written in descending order of the degree of its terms.