[tex]f(x)=\frac{x^4-x^3-6x^2+6x}{x^3-x}\\\\\\x^3-x\neq0\\\\x(x^2-1)\neq0\\\\x\neq0\ \vee \ x^2-1\neq0\\\\x\neq0\ \vee \ x^2\neq1\\\\x\neq0 \vee \ x\neq1\ \vee \ x\neq-1\\\\\\D:x \in R\setminus \{-1;0;1\}\\\\[/tex]
[tex]f(x)=\frac{x^4-x^3-6x^2+6x}{x^3-x}\\\\f(x)=\frac{x^3(x-1)-6x(x-1)}{x(x^2-1)}\\\\f(x)=\frac{(x^3-6x)(x-1)}{x(x+1)(x-1)}\\\\f(x)=\frac{x(x^2-6)}{x(x+1)}\\\\f(x)=\frac{x^2-6}{x+1}\\\\[/tex]
[tex]f(x)=\frac{x^2-6}{x+1}\\\\f(\sqrt{7})=\frac{(\sqrt7)^2-6}{\sqrt{7}+1}\\\\f(\sqrt{7})=\frac{1}{\sqrt{7}+1}\\\\f(\sqrt{7})=\frac{1}{\sqrt{7}+1}*\frac{\sqrt{7}-1}{\sqrt{7}-1}\\\\f(\sqrt{7})=\frac{\sqrt{7}-1}{6}\\\\[/tex]
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[tex]f(x)=\frac{x^4-x^3-6x^2+6x}{x^3-x}\\\\\\x^3-x\neq0\\\\x(x^2-1)\neq0\\\\x\neq0\ \vee \ x^2-1\neq0\\\\x\neq0\ \vee \ x^2\neq1\\\\x\neq0 \vee \ x\neq1\ \vee \ x\neq-1\\\\\\D:x \in R\setminus \{-1;0;1\}\\\\[/tex]
[tex]f(x)=\frac{x^4-x^3-6x^2+6x}{x^3-x}\\\\f(x)=\frac{x^3(x-1)-6x(x-1)}{x(x^2-1)}\\\\f(x)=\frac{(x^3-6x)(x-1)}{x(x+1)(x-1)}\\\\f(x)=\frac{x(x^2-6)}{x(x+1)}\\\\f(x)=\frac{x^2-6}{x+1}\\\\[/tex]
[tex]f(x)=\frac{x^2-6}{x+1}\\\\f(\sqrt{7})=\frac{(\sqrt7)^2-6}{\sqrt{7}+1}\\\\f(\sqrt{7})=\frac{1}{\sqrt{7}+1}\\\\f(\sqrt{7})=\frac{1}{\sqrt{7}+1}*\frac{\sqrt{7}-1}{\sqrt{7}-1}\\\\f(\sqrt{7})=\frac{\sqrt{7}-1}{6}\\\\[/tex]