Simplifying 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.

Tags

CCSS.HSA.APR.D.6

Front

How do you factor a polynomial?

Back

To factor a polynomial, you find the roots of the polynomial and express it as a product of its linear 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).

Tags

CCSS.HSA.APR.C.4

Front

How do you simplify the expression \( \frac{x^2 - 25}{x^2 - 6x + 5} \)?

Back

Factor the numerator as (x - 5)(x + 5) and the denominator as (x - 1)(x - 5), then cancel the common factor to get \( \frac{x + 5}{x - 1} \).

Tags

CCSS.HSA.APR.D.6

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.

Tags

CCSS.HSA.APR.D.6

Front

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

Back

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

Tags

CCSS.HSA.APR.D.6

Front

How do you handle rational expressions with restrictions?

Back

You must identify values that make the denominator zero and exclude them from the domain of the expression.

Front

What is the result of simplifying \( \frac{x^2 - 4x - 45}{x^2 - 81} \)?

Back

The result is \( \frac{x + 5}{x + 9} \) after factoring and canceling common factors.

Tags

CCSS.HSA.APR.D.6

Front

What is the factored form of \( x^2 + 6x \)?

Back

The factored form is \( x(x + 6) \).