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 complex fraction?

Back

To simplify a complex fraction, multiply the numerator and the denominator by the least common denominator (LCD) of the fractions involved.

Front

What is the process for multiplying rational expressions?

Back

To multiply rational expressions, multiply the numerators together and the denominators together, then simplify if possible.

Front

What is the formula for factoring a difference of squares?

Back

The formula for factoring a difference of squares is a^2 - b^2 = (a - b)(a + b).

Front

How do you divide rational expressions?

Back

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

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest expression that can be used as a common denominator for a set of fractions.

Front

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

Back

Canceling common factors in rational expressions simplifies the expression and helps to reduce it to its simplest form.

Front

What is the result of multiplying (x+2)/(4) by (x-1)/(x+8)?

Back

The result is (x^2 + x - 2)/(4(x + 8)).

Front

How do you identify vertical asymptotes in rational functions?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, provided those values do not also make the numerator zero.

Front

What is the difference between a removable and a non-removable discontinuity?

Back

A removable discontinuity occurs when a factor cancels out in a rational expression, while a non-removable discontinuity occurs when the factor remains in the denominator.