Skip to main content
Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 79
Chapter 1, Problem 79

Simplify each complex fraction. m−1m2−41m+2\(\frac{m - \frac{1}{m^2 - 4}\)}{\(\frac{1}{m + 2}\)}

Verified step by step guidance
1
Identify the complex fraction: the numerator is \(m - \frac{1}{m^{2} - 4}\) and the denominator is \(\frac{1}{m + 2}\).
Recognize that \(m^{2} - 4\) is a difference of squares and factor it as \((m - 2)(m + 2)\).
Rewrite the numerator as \(m - \frac{1}{(m - 2)(m + 2)}\) to have a common denominator for the terms in the numerator.
Express \(m\) as \(\frac{m(m - 2)(m + 2)}{(m - 2)(m + 2)}\) so that both terms in the numerator share the denominator \((m - 2)(m + 2)\), then combine them into a single fraction.
Divide the resulting numerator fraction by the denominator \(\frac{1}{m + 2}\) by multiplying the numerator fraction by the reciprocal of the denominator, which is \((m + 2)\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complex Fractions

A complex fraction is a fraction where the numerator, denominator, or both contain fractions themselves. Simplifying involves rewriting the expression as a single fraction by finding common denominators or multiplying by the reciprocal of the denominator.
Recommended video:
05:33
Complex Conjugates

Factoring Quadratic Expressions

Factoring involves expressing a quadratic expression as a product of simpler binomials. For example, m^2 - 4 is a difference of squares and factors into (m - 2)(m + 2), which helps simplify fractions by canceling common factors.
Recommended video:
06:08
Solving Quadratic Equations by Factoring

Multiplying by the Reciprocal

To divide by a fraction, multiply by its reciprocal. In this problem, dividing by 1/(m + 2) is equivalent to multiplying by (m + 2), which simplifies the complex fraction into a simpler algebraic expression.
Recommended video:
Guided course
04:15
Multiply Polynomials Using the Distributive Property
Related Practice
Textbook Question

In the decimal number 367.9412, name the digit that has each place value. (a) tens (b) tenths (c) thousandths (d) ones or units (e) hundredths

1
views
Textbook Question

Determine whether each statement is true or false. ∅ ∪ ∅ = ∅

1
views
Textbook Question

In the decimal number 367.9412, name the digit that has each place value. (a) tens (b) tenths (c) thousandths (d) ones or units (e) hundredths

Textbook Question

Evaluate each expression. (-4)1/2

2
views
Textbook Question

In the decimal number 367.9412, name the digit that has each place value. (a) tens (b) tenths (c) thousandths (d) ones or units (e) hundredths

Textbook Question

Perform each division. See Examples 7 and 8. (9y2+12y-5)/(3y)