The following mathematical expression needs to be simplified:\[ \frac{5}{x^2 - 5x} - \frac{x}{5x - 25} \]In this equation, two rational expressions are being subtracted from each other. Each rational expression consists of a numerator and a denominator:1. The first fraction: - Numerator: 5 - Denominator: \( x^2 - 5x \)2. The second fraction: - Numerator: x - Denominator: \( 5x - 25 \)To proceed with simplifying this expression, one may start by factoring the denominators.### Factoring the Denominators1. For the denominator \( x^2 - 5x \): \[ x^2 - 5x = x(x - 5) \]2. For the denominator \( 5x - 25 \): \[ 5x - 25 = 5(x - 5) \]### Simplified ExpressionWith these factorizations, the expression becomes:\[ \frac{5}{x(x - 5)} - \frac{x}{5(x - 5)} \]Combining the two fractions over a common denominator, which would be \( 5x(x - 5) \):\[ \frac{5 \cdot 5 - x \cdot x}{5x(x - 5)} = \frac{25 - x^2}{5x(x - 5)} \]### Final NotesThis simplified fraction can then be further analyzed or evaluated based on the specific values of \( x \), keeping in mind the restrictions where the denominator cannot be zero. In other words, \( x \neq 0 \) and \( x \neq 5 \) to avoid division by zero.

the given expression is: we have to simplify the given expression.

Answered: х2 —5х 5x 25

х2 —5х 5x 25

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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