Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Concept explainers

Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
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The equation displayed is: \[ \frac{10}{x^2 - 2x} + \frac{4}{x} = \frac{5}{x - 2} \] This is a rational equation consisting of three fractional terms, each with polynomial expressions in their denominators. The goal is often to find the values of \( x \) that satisfy this equality. - The first term is the fraction \(\frac{10}{x^2 - 2x}\). - The second term is \(\frac{4}{x}\). - The right side of the equation is \(\frac{5}{x - 2}\). To solve this equation, one approach is to find a common denominator and eliminate the fractions. Consider the restrictions on \( x \) to avoid division by zero.
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Transcribed Image Text:The equation displayed is: \[ \frac{10}{x^2 - 2x} + \frac{4}{x} = \frac{5}{x - 2} \] This is a rational equation consisting of three fractional terms, each with polynomial expressions in their denominators. The goal is often to find the values of \( x \) that satisfy this equality. - The first term is the fraction \(\frac{10}{x^2 - 2x}\). - The second term is \(\frac{4}{x}\). - The right side of the equation is \(\frac{5}{x - 2}\). To solve this equation, one approach is to find a common denominator and eliminate the fractions. Consider the restrictions on \( x \) to avoid division by zero.
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