algebra precalculus - Rational Equations: What are Excluded …
2019年3月20日 · Rational Equations: What are Excluded Values? ... Any rational expression with the denominator being $ 0 ...
Why aren't equations with rational expressions equivalent to …
2022年12月24日 · When dealing with equations, although it is common practice to perform operations such as multiplication and division to both sides of an equation, we need to be mindful that such operations can introduce or eliminate solutions.
Rational word problem: comparing two rational functions
2018年5月4日 · So far we have learned how to solve rational equations, inequalities, and rates of change. I have not encountered a word problem like this and am unsure where to start. Graphing calculators are not allowed but I did look at the graphs for both functions and they both have the same asymptotes and origin at (0,0) and share the points (-1.4142, -5 ...
algebra precalculus - Losing Solutions to a Rational Equation ...
2020年10月31日 · The question is now reduced to solving a linear equation and the solutions to this linear equation will be the solutions to the rational equation (assuming they don't create a zero in any of the denominators).
Why do we get extraneous roots when solving radical or rational …
2022年4月29日 · We all know that we might get extraneous solutions when solving certain equations like rational equations and equations with radicals. In high school, teachers tell students that they should always check the solutions they obtained when solving equations like these because extraneous roots might appear.
When do we specify restrictions in rational expressions or equations
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Finding the equation of a rational function from a set of points
2019年7月11日 · What I did was use two of the points to build a system of equations and solve for a and b. The function I come up with passes through the points but has oscillations in between the points and does not have the shape of a log/square root function. I was recommended to use Lineweaver-Burke plot to deal with this problem.
abstract algebra - When a system of rational linear equations have ...
2014年8月28日 · Note that row reduction does not necessitate the use of non-rational numbers (only the four basic arithmetic operations are used). At that point the solutions of the system take the form where the values some of the unknowns can be chosen freely, and the rest are rational linear combinations of the freely chosen ones. $\endgroup$
education - "Real world" applications of rational functions ...
2014年8月16日 · A "real world" application of rational functions is the "Thin Lens Equation" which relates focal length, object distance, and real image distance. It is as practical as it gets. Cameras, eyeballs, magnifying glasses, etc all operate using this principle in some capacity. The derivation of it is straight forward and only uses similar triangles.
Finding solution set of rational equations with constants
2017年8月30日 · So there are apparently 2 different ways to solve equations with absolute values... 2 Are there ways to solve miscellaneous equations such as $\sin x=\log [x]$ without drawing the graphs?