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 is factoring in algebra?

Back

Factoring is the process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.

Front

What does it mean to cancel in a fraction?

Back

Canceling in a fraction means removing common factors from the numerator and denominator.

Front

Simplify: (x^2 + 6x + 8)/(x^2 - x - 6)

Back

(x + 4)/(x - 3)

Front

What is the first step in simplifying (x + 5)(x - 5)/(x + 5)(x - 2)?

Back

The first step is to factor out the common term (x + 5) from the numerator and denominator.

Front

Simplify: (x + 5)(x - 5)/(x + 5)(x - 2)

Back

(x - 5)/(x - 2)

Front

What is an algebraic fraction?

Back

An algebraic fraction is a fraction where the numerator and/or the denominator are algebraic expressions.

Front

What does it mean if a rational expression can't be simplified?

Back

It means there are no common factors in the numerator and denominator that can be canceled.

Front

Simplify: 6/(x + 4)

Back

6/(x + 4) is already in its simplest form.