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 a rational expression?

Back

Cancelling means removing common factors from the numerator and denominator.

Front

What is the first step in simplifying (3x^2y)/(6xy^2)?

Back

Factor out the common terms: 3x^2y = 3xy * x and 6xy^2 = 3xy * 2y.

Front

Simplify the expression (x^2 - 9)/(x + 3).

Back

The simplified form is (x - 3) because x^2 - 9 is a difference of squares.

Front

What is the simplified form of (x + 6)/(x + 4)?

Back

The expression cannot be simplified further.

Front

What is the result of simplifying (x + 6)/(x - 5)?

Back

The expression remains (x + 6)/(x - 5) as it cannot be simplified.

Front

What does it mean if a rational expression cannot be simplified?

Back

It means there are no common factors in the numerator and denominator.

Front

What is the simplified form of (x^2 - 1)/(x + 1)?

Back

The simplified form is (x - 1) because x^2 - 1 is a difference of squares.

Front

How do you identify common factors in rational expressions?

Back

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