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.

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

How do you factor the expression x^2 - 81?

Back

x^2 - 81 can be factored as (x - 9)(x + 9) using the difference of squares formula.

Front

What is the first step in simplifying (x^2 - 81)/(x^2 - 9)?

Back

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

Front

What is the simplified form of (x^2 - 81)/(x^2 - 9)?

Back

The simplified form is (x - 9)/(x + 3) after factoring.

Front

How do you simplify the expression 15x^2/5x^3?

Back

You simplify it by dividing the coefficients and subtracting the exponents of x, resulting in 3/x.

Front

What is the importance of identifying common factors in rational expressions?

Back

Identifying common factors allows you to cancel them out, simplifying the expression.

Front

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

Back

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

Front

What does it mean if a rational expression is undefined?

Back

A rational expression is undefined when its denominator equals zero.