Modified Rational Expressions & Equations - Honors

Front

What are excluded values in a rational expression?

Back

Excluded values are values that make the denominator equal to zero. They must be identified before canceling any like terms in the expression.

Front

How do you determine excluded values for the expression \( \frac{x-2}{3x} \)?

Back

Set the denominator equal to zero: 3x = 0. Thus, x = 0 is an excluded value.

Front

What is the process to solve a rational equation by cross-multiplying?

Back

To solve a rational equation, cross-multiply the numerators and denominators. For example, for \( \frac{a}{b} = \frac{c}{d} \), cross-multiply to get \( a \cdot d = b \cdot c \).

Front

What does it mean for a rational expression to be undefined?

Back

A rational expression is undefined when its denominator equals zero. For example, \( \frac{1}{x-2} \) is undefined when x = 2.

Front

What is the first step in simplifying a rational expression?

Back

The first step is to factor both the numerator and the denominator to identify any common factors.

Front

How do you find the excluded values for the expression \( \frac{x^2 - 4}{x^2 - 1} \)?

Back

Set the denominator equal to zero: \( x^2 - 1 = 0 \). This gives excluded values of x = 1 and x = -1.

Front

What is the significance of canceling like terms in rational expressions?

Back

Canceling like terms simplifies the expression but does not change the excluded values, which must be identified before canceling.

Front

Solve the equation \( \frac{x-2}{3x} = \frac{1}{3x} + 2 \).

Back

The solution is \( x = -\frac{3}{5} \).

Front

What are the excluded values for the expression \( \frac{1}{x^2 - 4} \)?

Back

The excluded values are x = 2 and x = -2, as these make the denominator zero.

Front

What does it mean to solve a rational equation?

Back

Solving a rational equation involves finding the value(s) of the variable that make the equation true, ensuring that the solutions do not make the denominator zero.