Simplify each fraction. Assume that no denominators are 0 . (25-x^2)/(x^2+10 x+25)

Name: Problem 26, Chapter 0: College Algebra
Uploaded: 2020-07-16T00:38:34-08:00
Duration: 2 min 13 s
Channel: Casey Evans
Description: Simplify each fraction. Assume that no denominators are 0 . (25-x^2)/(x^2+10 x+25)

step 1 We have a difference of squares on top and then some factoring to do down bot Let's save some ti

Simplify each fraction. Assume that no denominators are 0 ....

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Key Concepts

Factorization

Factorization is the process of rewriting a polynomial as a product of its simpler component factors. This technique is essential for simplifying algebraic expressions and solving equations by revealing common factors that can be canceled or used to set factors equal to zero.

Difference of Squares

A difference of squares is a special factoring pattern where an expression is written as a squared term minus another squared term. It factors into the product of two binomials where one is the sum and the other is the difference of the square roots, expressed as (a - b)(a + b).

Perfect Square Trinomials

A perfect square trinomial is a quadratic expression that can be written as the square of a binomial. It follows the pattern a^2 + 2ab + b^2, which factors neatly into (a + b)^2, simplifying the process of manipulation and cancellation in rational expressions.

Simplifying Rational Expressions

Simplifying rational expressions involves factoring both the numerator and the denominator to identify and cancel common factors, provided that the values making the denominator zero are excluded. This process reduces the expression to its lowest terms and facilitates further operations or solutions.

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