Adding and Subtracting 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

What are the steps to add rational expressions with different denominators?

Back

1. Find a common denominator. 2. Rewrite each expression with the common denominator. 3. Add the numerators. 4. Simplify the resulting expression.

Front

What is the restriction in the expression \( \frac{1}{x-3} \)?

Back

The restriction is that \( x \) cannot equal 3, as it would make the denominator zero.

Front

How do you simplify the expression \( \frac{7}{x+2}-\frac{4}{x-5} \)?

Back

1. Find a common denominator: \( (x+2)(x-5) \). 2. Rewrite each fraction. 3. Combine and simplify.

Front

What is the result of adding \( \frac{2}{x^2-x-20} \) and \( \frac{3}{x^2+7x+12} \)?

Back

The result is \( \frac{5x-9}{(x-5)(x+4)(x+3)}; \ x \ne -4, -3, 5 \).

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 make the denominator zero, which are not allowed.

Front

What is the first step in subtracting rational expressions?

Back

The first step is to find a common denominator for the expressions being subtracted.

Front

How do you factor the expression \( x^2 - x - 20 \)?

Back

The expression factors to \( (x-5)(x+4) \).

Front

What is the simplified form of \( \frac{3x-43}{(x+2)(x-5)} \)?

Back

The expression is already in its simplified form, with restrictions \( x \ne -2, 5 \).

Front

What is the importance of simplifying rational expressions?

Back

Simplifying rational expressions makes them easier to work with and helps identify restrictions and potential solutions.