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 does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

What is the first step in simplifying (5x^2 + 21x + 4) / (25x + 100)?

Back

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

Front

What is the simplified form of (5x^2 + 21x + 4) / (25x + 100)?

Back

The simplified form is (5x + 1) / 25.

Front

What is the simplified form of (x-9)/(x+9)?

Back

The simplified form is 1/(x-9).

Front

How do you simplify (2x^2-98)/(2x^2+18x+28)?

Back

Factor both the numerator and the denominator to get (x-7)/(x+2).

Front

What is the simplified form of (x + 5)(x - 5) / (x + 5)(x - 2)?

Back

The simplified form is (x - 5) / (x - 2).

Front

What does it mean to cancel in a rational expression?

Back

Canceling means removing common factors from the numerator and denominator.

Front

What is the simplified form of 5-x/x-5?

Back

The simplified form is -1.