Operations with 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 the first step in adding or subtracting rational expressions?

Back

The first step is to find a common denominator.

Front

What is the formula for multiplying rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together.

Front

What is the formula for dividing rational expressions?

Back

To divide rational expressions, multiply by the reciprocal of the divisor.

Front

How do you find the least common denominator (LCD) of two rational expressions?

Back

The LCD is the least common multiple of the denominators of the rational expressions.

Front

What happens to a rational expression if you multiply the numerator and denominator by the same non-zero value?

Back

The value of the rational expression remains unchanged.

Front

What is the result of subtracting (x+2)/(x-3) from (x-1)/(x+3)?

Back

The result is ((x-1)(x-3) - (x+2)(x+3)) / ((x-3)(x+3)).

Front

What is the domain of a rational expression?

Back

The domain is all real numbers except where the denominator equals zero.

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.