Question

Simplify each rational expression. $$ \frac{y^{2}-10 y z+24 z^{2}}{y^{2}-5 y z+4 z^{2}} $$

Name: Problem 38, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2021-03-25T21:16:04-08:00
Duration: 1 min 3 s
Channel: Prashansha Kaushik
Description: Simplify each rational expression. (y^2-10 y z+24 z^2)/(y^2-5 y z+4 z^2)

   Simplify each rational expression.
$$
\frac{y^{2}-10 y z+24 z^{2}}{y^{2}-5 y z+4 z^{2}}
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 38

Instant Answer

Solved by Expert Prashansha Kaushik

03/25/2021

Step 1

Numerator: $y^2 - 10yz + 24z^2 = (y - 6z)(y - 4z)$ Denominator: $y^2 - 5yz + 4z^2 = (y - 4z)(y - z)$ Show more…

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Simplify each rational expression. $$ \frac{y^{2}-10 y z+24 z^{2}}{y^{2}-5 y z+4 z^{2}} $$

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Key Concepts

Factoring Quadratic Polynomials

This involves rewriting quadratic expressions as the product of two binomials. It is a key algebraic technique that enables the simplification of expressions and the solution of quadratic equations, especially when the quadratic factors neatly.

Common Factor Cancellation in Rational Expressions

This concept refers to the process of identifying and canceling factors that appear in both the numerator and the denominator of a rational expression. This simplification step is fundamental in algebra, as it allows one to reduce the expression to its simplest form.

Domain Restrictions

When simplifying rational expressions, it is important to consider the values of the variable that might make the denominator equal to zero. Excluding these values prevents undefined expressions and ensures that the simplified form is equivalent to the original expression where it is defined.

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