Mathematics: Analyze the rational function: f(x) = (x^2 - 4)/(x^3 - 3x^2 - 10x)

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Analyze the rational function: f(x) = (x^2 - 4)/(x^3 - id2413676422, jacobmclawhorn3001

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bethzabezarahi

09.07.2021

Mathematics

The function $f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}$ has a zero: x = 2 , and two poles: x = 0 and x = 5 .

Step-by-step explanation:

Let be $f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}$ a rational function armed with polynomial function. We proceed to factor the expression to the find the zeros and poles of the rational function:

1) $f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}$ Given

2) $f(x) = \frac{(x + 2)\cdot (x-2)}{x\cdot (x^{2}-3\cdot x -10)}$ $a^{2} - b^{2} = (a + b)\cdot (a - b)$ /Associative, commutative and distributive properties.

3) $f(x) = \frac{(x+2)\cdot (x-2)}{x\cdot (x-5)\cdot (x+2)}$ $x^{2} -(a+b)\cdot x + a\cdot b = (x-a)\cdot (x-b)$

4) $f(x) = \frac{x-2}{x\cdot (x-5)}$ Commutative property/Existence of multiplicative inverse/Modulative property/Result

The function $f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}$ has a zero: x = 2 , and two poles: x = 0 and x = 5 .

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Analyze the rational function: f(x) = (x^2 - 4)/(x^3 - 3x^2 - 10x)

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