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 the expression (n-6)/(n-7)?

Back

The first step is to check if the numerator and denominator can be factored further.

Front

What is the simplified form of 1/(n-7)?

Back

The simplified form is 1/(n-7) as it cannot be simplified further.

Front

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

Back

Identifying common factors allows you to simplify the expression, making calculations easier.

Front

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

Back

The expression is undefined when m=3 because the denominator becomes zero.

Front

How do you determine if a rational expression is undefined?

Back

A rational expression is undefined when its denominator equals zero.

Front

What is the simplified form of 7/(m-3)?

Back

The simplified form is 7/(m-3) as it cannot be simplified further.

Front

What is the result of factoring 16x^2 + 18x + 12?

Back

The factored form is 2(8x^2 + 9x + 6).