Write each rational expression in lowest terms. (30-35 x)/(7...

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

Even after cancelling common factors from a rational expression, it is important to remember the domain restrictions. These restrictions arise from values that cause the original denominator to be zero, which are not allowed, ensuring that the simplified form is equivalent to the original for all values within its domain.

Canceling Common Factors

After factoring both the numerator and the denominator, any factors they have in common can be cancelled to simplify the rational expression. This process reduces the expression to its lowest terms, but it must be done carefully to ensure that the operations are valid and that restrictions from the original domain are maintained.

Factoring Polynomials

Factoring polynomials involves expressing a polynomial as a product of simpler polynomials or irreducible factors. This technique is essential when working with rational expressions, as it helps to identify common factors in the numerator and denominator that can be cancelled to simplify the expression.

Rational Expressions

A rational expression is a ratio of two polynomials. These expressions share many properties with numerical fractions, and simplifying them involves rewriting them in an equivalent form where the numerator and denominator have no common factors, similar to reducing a fraction to its simplest form.

Transcript

Please give Ace some feedback