Simplifying Rational Expressions Review

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 are the restrictions on a rational expression?

Back

Restrictions are values that make the denominator zero, which are not allowed in the expression.

Front

What is the process for dividing rational expressions?

Back

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

Front

How do you find the inverse of a function graphically?

Back

The inverse of a function can be found by reflecting the graph across the line y = x.

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.

Front

What does it mean to state the restrictions of a rational expression?

Back

Stating the restrictions means identifying the values of the variable that would make the denominator zero.

Front

How do you simplify complex fractions?

Back

To simplify complex fractions, find a common denominator for the fractions in the numerator and denominator, then simplify.

Front

What is the result of simplifying the expression \( \frac{x^8y^{12}}{x^4y^{15}} \)?

Back

The result is \( \frac{x^4}{y^3} \).

Front

What is the result of dividing \( \frac{1-x^2}{2x^2-10x-12} \) by \( \frac{2x-2}{6} \)?

Back

The result is \( -\frac{3}{2(x-6)} \).