Multiply, and then simplify, if possible. (m^2-2 m-3)/(2 m+4) ·(m^2-4)/(m^2+3 m+2)

Name: Problem 29, Chapter 7: Elementary and Intermediate Algebra
Uploaded: 2020-03-28T14:20:55-08:00
Duration: 1 min 58 s
Channel: Joshua Eastwood
Description: Multiply, and then simplify, if possible. (m^2-2 m-3)/(2 m+4) ·(m^2-4)/(m^2+3 m+2)

step 1 We're given a rational expression to multiply. So it's m squared minus 2m minus 3 divided by 2m

Question

Multiply, and then simplify, if possible. $\frac{m^{2}-2 m-3}{2 m+4} \cdot \frac{m^{2}-4}{m^{2}+3 m+2}$

   Multiply, and then simplify, if possible.
$\frac{m^{2}-2 m-3}{2 m+4} \cdot \frac{m^{2}-4}{m^{2}+3 m+2}$

Elementary and Intermediate Algebra

Alan S. Tussy, R.… 5th Edition

Chapter 7, Problem 29

Instant Answer

Solved by Expert Joshua Eastwood

03/28/2020

Step 1

The first expression $\frac{m^{2}-2 m-3}{2 m+4}$ can be factored as $\frac{(m-3)(m+1)}{2(m+2)}$. The second expression $\frac{m^{2}-4}{m^{2}+3 m+2}$ can be factored as $\frac{(m-2)(m+2)}{(m+2)(m+1)}$. Show more…

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Multiply, and then simplify, if possible. $\frac{m^{2}-2 m-3}{2 m+4} \cdot \frac{m^{2}-4}{m^{2}+3 m+2}$

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Key Concepts

Rational Expressions

Rational expressions are fractions in which both the numerator and the denominator are polynomials. They require careful manipulation, including factorization, to simplify them and to understand the restrictions on the variable values (the domain).

Polynomial Factoring

Polynomial factoring involves rewriting a polynomial as a product of its simpler factors, such as linear or irreducible quadratic factors. This process is essential for simplifying rational expressions by allowing the cancellation of common factors between numerators and denominators.

Multiplication of Rational Expressions

Multiplying rational expressions entails multiplying the numerators together and the denominators together. After performing the multiplication, the resulting expression is simplified further by factoring and canceling any common factors to achieve the simplest form.

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