Simplify the expression (3-x)/(x^2-5 x+6) (A) (1)/(x+2) (B) (1)/(x-2) (C) (-1)/(x+2) (D) (-1)/(x

step 1 To simplify this expression, what we want to do is factor the numerator and denominator, and the

Simplify the expression (3-x)/(x^2-5 x+6) (A) (1)/(x+2) (B)...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Domain Restrictions

When simplifying expressions, it is important to note values for the variable that make any denominator zero. These restrictions must be considered to ensure that the simplification is valid over the intended domain.

Sign Manipulation

Algebraic expressions sometimes require rewriting terms by factoring out negative signs to reveal hidden common factors. Recognizing and correctly managing these sign changes is crucial for accurate simplification.

Factoring Quadratic Expressions

This involves rewriting a quadratic polynomial as a product of binomials. It is a fundamental technique in algebra that simplifies expressions and equations, making further operations like cancellation and solving possible.

Simplifying Rational Expressions

Rational expressions are fractions with polynomials in the numerator and denominator. Simplifying them typically involves factoring both parts and then cancelling any common factors, with the understanding that factors cancelled must not be zero.

Cancellation of Common Factors

In algebra, when the same factor appears in both the numerator and the denominator, it can be cancelled provided that it is not equal to zero. This step is essential in reducing expressions to their simplest form.

Transcript

Please give Ace some feedback