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

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 for a rational expression to be undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

Simplify: 20x³/(5x+10)

Back

4x³/(x+2)

Front

What is the first step in simplifying the expression 20x³/(5x+10)?

Back

Factor the denominator: 5x + 10 = 5(x + 2).

Front

Simplify: (x-9)/(x+9)

Back

1/(x+9) (if x ≠ -9) or (x-9)/(x+9) (if x ≠ 9) depending on context.

Front

What is the result of simplifying 7(m+6)/(m-3)?

Back

7/(m-3) (if m ≠ 3) or 7(m+6)/(m-3) (if m ≠ -6) depending on context.

Front

Identify the value that makes the expression 20x/(5x+10) undefined.

Back

-2 (since 5x + 10 = 0 when x = -2).

Front

What is the simplified form of -9a^3/-a^6?

Back

9/a^3.

Front

What is the significance of factoring in simplifying rational expressions?

Back

Factoring allows you to identify and cancel common factors in the numerator and denominator.