Question

Simplify the expression. $$\frac{x}{x+6} \div \frac{x+1}{x+6}$$

   Simplify the expression.
$$\frac{x}{x+6} \div \frac{x+1}{x+6}$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 12, Problem 87

Instant Answer

Solved by Expert Amy Jiang

09/01/2020

Step 1

This gives us: $$\frac{x}{x+6} \times \frac{x+6}{x+1}$$ Show more…

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Simplify the expression. $$\frac{x}{x+6} \div \frac{x+1}{x+6}$$

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Key Concepts

Division of Fractions

Division of fractions involves multiplying by the reciprocal of the divisor. This means that when one fraction is divided by another, you can flip the second fraction and change the operation to multiplication. This method is fundamental in arithmetic and algebra for simplifying complex fractional expressions.

Multiplicative Inverse

The multiplicative inverse, or reciprocal, of a number or expression is what you multiply that number by to obtain 1. In the context of fractions, the reciprocal of a fraction is obtained by swapping its numerator and denominator. This concept is crucial when rewriting a division of fractions as a multiplication problem.

Simplification of Rational Expressions

Simplifying rational expressions involves rewriting the expression in its simplest form by canceling any common factors in the numerator and denominator. This process may require factoring polynomials and being careful not to cancel terms that would affect the domain of the expression.

Domain Restrictions

When working with rational expressions, it is important to consider the domain restrictions; that is, the values that make any denominator zero must be excluded. Recognizing and stating these restrictions ensures that the simplified expression is equivalent to the original for all valid inputs.

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