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

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 is the difference of squares?

Back

The difference of squares is a special product that can be expressed as a^2 - b^2 = (a - b)(a + b).

Front

How do you simplify (x^2 - 9)/(x + 3)?

Back

Factor the numerator: (x - 3)(x + 3)/(x + 3). Cancel the common factor: x - 3.

Front

What is the result of simplifying (x^2 - 4)/(x - 2)?

Back

Factor the numerator: (x - 2)(x + 2)/(x - 2). Cancel the common factor: x + 2.

Front

What is the simplified form of (x + 5)/(x + 5)?

Back

The simplified form is 1, as long as x + 5 ≠ 0.

Front

How do you simplify 1/(n - 7)?

Back

1/(n - 7) is already in its simplest form.

Front

What is the simplified form of (n^2 - 49)/(n - 7)?

Back

Factor the numerator: (n - 7)(n + 7)/(n - 7). Cancel the common factor: n + 7.