Question

Simplify the expression. $$\frac{4}{x+1}+\frac{2 x-2}{x+1}$$

   Simplify the expression.
$$\frac{4}{x+1}+\frac{2 x-2}{x+1}$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 11, Problem 11

Instant Answer

Solved by Expert Raushan Kumar

09/22/2020

Step 1

So, we can combine the numerators over the common denominator. $$\frac{4}{x+1}+\frac{2 x-2}{x+1} = \frac{4+(2x-2)}{x+1}$$ Show more…

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Simplify the expression. $$\frac{4}{x+1}+\frac{2 x-2}{x+1}$$

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Key Concepts

Rational Expressions

Rational expressions are fractions where the numerator and/or the denominator are polynomials. Understanding how to manipulate these expressions is crucial in algebra, particularly when performing operations such as addition, subtraction, multiplication, and division on them.

Common Denominator

A common denominator is essential when adding or subtracting fractions. In rational expressions, if the denominators are the same, you can combine the numerators directly, which simplifies the process of adding or subtracting the expressions.

Combining Like Terms

When working with polynomials in the numerator, combining like terms is a critical step in simplification. This process involves adding or subtracting coefficients of terms that have the same variable raised to the same power.

Factoring

Factoring involves rewriting a polynomial as a product of its factors. This technique can simplify rational expressions by revealing common factors in the numerator and denominator that can be canceled, thereby reducing the expression to its simplest form.

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