Question

Simplify each expression. $$ \frac{2 x^{2}-8}{4 x-8} $$

   Simplify each expression.
$$
\frac{2 x^{2}-8}{4 x-8}
$$

Algebra A Combined Function

Algebra A Combined Function

Elayn Martin-Gay 4th Edition

Chapter 7, Problem 49

Instant Answer

Solved by Expert Victor Salazar

02/07/2022

Step 1

In the numerator, the common factor is 2, and in the denominator, the common factor is 4. So, we can rewrite the expression as: $$ \frac{2(x^{2}-4)}{4(x-2)} $$ Show more…

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Simplify each expression. $$ \frac{2 x^{2}-8}{4 x-8} $$

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Key Concepts

Polynomial Factoring

This concept involves expressing a polynomial as the product of its simpler factors. It is a fundamental algebraic technique used to simplify expressions and solve equations, where identifying a common factor among the terms can help in rewriting the polynomial in a factored form.

Simplification of Rational Expressions

Simplifying rational expressions involves reducing a fraction composed of polynomials to its simplest form. This process typically includes factoring both the numerator and the denominator and then canceling out any common factors, while also emphasizing the importance of considering any restrictions on the variable.

Cancellation of Common Factors

Once both the numerator and the denominator of a rational expression are factored, identical factors present in both can be canceled. This cancellation step helps in reducing the expression to a simpler form but should be done carefully, keeping in mind that the canceled factors may indicate values that are not allowed in the domain.

Domain Restrictions

Domain restrictions refer to the values of the variable that must be excluded from the simplified expression to avoid undefined situations, such as division by zero. When canceling factors in a rational expression, it is essential to state these restrictions to maintain the equivalence of the simplified expression with the original.

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