Question

$\frac{25}{m^{2}-9 m}=\frac{?}{m(m-9)(m+8)}$

   $\frac{25}{m^{2}-9 m}=\frac{?}{m(m-9)(m+8)}$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 6, Problem 66

Instant Answer

Solved by Expert Victor Salazar

02/14/2022

Step 1

So, we have: \[\frac{25(m+8)}{m^{2}-9m(m+8)}=\frac{?}{m(m-9)(m+8)}\] Show more…

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$\frac{25}{m^{2}-9 m}=\frac{?}{m(m-9)(m+8)}$

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Key Concepts

Factoring Algebraic Expressions

This concept involves rewriting a polynomial as a product of its factors. In algebra, recognizing and extracting common factors, such as a variable that appears in all terms, is essential for simplifying expressions and solving equations. Factoring lays the groundwork for other operations such as simplifying rational expressions or performing partial fractions decomposition.

Common Denominator Identification

A common denominator is used when comparing or combining fractions with different denominators. In rational expressions, identifying or creating a common denominator allows one to rewrite fractions so that they have the same denominator, which is a key step in equating or adding fractions, and for simplifying expressions correctly.

Equivalent Rational Expressions

Two rational expressions are equivalent if they simplify to the same form, even if their numerators and denominators look different initially. This involves multiplying or dividing the numerator and denominator by the same non-zero expression, ensuring that the value of the fraction remains unchanged. Understanding equivalent expressions is crucial for comparing fractions, solving rational equations, and verifying equality between different algebraic forms.

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