Question

simplifying rational expressions
rational expression definition: a fraction of two polynomials. ex: f(x) = (x+2)(x-1)
steps for simplifying rational expressions
step 1: simplify the numerator and denominator by ______________
step 2: divide out the ____________ factors if they appear in both the __________ and the ____________.
property: \\(\frac{a \cdot c}{b \cdot c} = \frac{a}{b}\\)
answers should always be left in ______________ form!

Explanation:

• Rational Expression Definition: A rational expression is a fraction of two polynomials. For example, \( f(x)=\frac{(x + 2)(x - 1)}{...} \) (the denominator is missing in the example but the key is it's a fraction of two polynomials).
• Step 1 for Simplifying: To simplify the numerator and denominator of a rational expression, we factor them (factoring polynomials into their prime or irreducible factors).
• Step 2 for Simplifying: After factoring, we divide out the common factors. These common factors must appear in both the numerator and the denominator.
• Final Form: When simplifying rational expressions, the answer should always be left in factored form (or simplified rational form, but factored is key here as we factor and then cancel common factors).

Answer:

• Rational Expression Definition: \(\boldsymbol{\text{fraction}}\)
• Steps for Simplifying Rational Expressions:
• Step 1: \(\boldsymbol{\text{factoring}}\)
• Step 2: \(\boldsymbol{\text{common}}\); \(\boldsymbol{\text{numerator}}\); \(\boldsymbol{\text{denominator}}\)
• Property (implied by the simplification): (The property shown is the cancellation of common factors, and the final form) \(\boldsymbol{\text{factored}}\) (or simplified rational, but factored is accurate for the steps)