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# What are rational functions?

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## Definition of a Rational function.A rational function is the ratio of two polynomial functions where the denominator polynomial is a non-zero polynomial. A rational function $\mathrm{R}\left(x\right)$ is of the form $\mathrm{R}\left(x\right)=\frac{\mathrm{P}\left(x\right)}{\mathrm{Q}\left(x\right)}$ Where, $\mathrm{P}\left(x\right)\mathrm{and}\mathrm{Q}\left(x\right)$ are the polynomial of the type $a{x}^{n}+b{x}^{n-1}+...\alpha x+\beta$ and $x$ belongs to some interval of real number such that $Q\left(x\right)\ne 0$The examples of rational functions are:$R\left(x\right)=\frac{2x+5}{x-1},x\ne 1$Here for $x=1$ denominator $\mathrm{Q}\left(x\right)=x-1=0$ thus the domain of $x$ such that $Q\left(x\right)\ne 0$ is $x\in \mathrm{ℝ}-\left\{1\right\}$ 2. $R\left(x\right)=\frac{{x}^{2}+5x-6}{{x}^{2}+2},x\in R$Here for$Q\left(x\right)\ne 0$ ,all $x\in \mathrm{ℝ}$, thus the domain of $x$ such that $Q\left(x\right)\ne 0$ is $x\in \left(-\infty ,\infty \right)$

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