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 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 does it mean to cancel in rational expressions?

Back

Cancelling means removing common factors from the numerator and denominator.

Front

What is the first step in simplifying the expression (x^2 - 1)/(x + 1)?

Back

Factor the numerator: (x - 1)(x + 1)/(x + 1).

Front

What is the simplified form of (x^2 - 4)/(x - 2)?

Back

The simplified form is (x + 2) when x ≠ 2.

Front

What is the restriction on the variable in the expression (x + 3)/(x - 2)?

Back

x cannot be equal to 2, as it would make the denominator zero.

Front

How do you identify common factors in rational expressions?

Back

Look for factors that appear in both the numerator and the denominator.

Front

What is the simplified form of (2x^2)/(4x)?

Back

The simplified form is (x/2) when x ≠ 0.

Front

What happens if you try to simplify (x^2)/(x^2)?

Back

The expression simplifies to 1, provided x ≠ 0.

Front

What is the importance of factoring in simplifying rational expressions?

Back

Factoring allows you to identify and cancel common factors, simplifying the expression.