[tex]f( \frac{3x-1}{x+2} )= \frac{x+1}{x-1} f(x)=?[/tex]. Created by Ilyasssssss. algebra-ru

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[tex]f( \frac{3x-1}{x+2} )= \frac{x+1}{x-1}

f(x)=?[/tex]

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NNNLLL54

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$f( \frac{3x-1}{x+2} )= \frac{x+1}{x-1} \; ,\; \; \; f(x)=?\\\\Zamena:\; \; t= \frac{3x-1}{x+2} \; \; \Rightarrow \; \; 3x-1=t(x+2)\\\\3x-1=tx+2t\\\\3x-tx=1+2t\\\\x(3-t)=1+2t\\\\x= \frac{1+2t}{3-t} \\\\ \frac{x+1}{x-1} = \frac{\frac{1+2t}{3-t}+1}{\frac{1+2t}{3-t}-1} = \frac{1+2t+3-t}{1+2t-3+t} = \frac{t+4}{3t-2} \; \; \Rightarrow\\\\f(t)= \frac{t+4}{3t-2}$

Так как от обозначения переменной (буквой х или буквой t )смысл формулы не измениться, то получим:

$f(x)=\frac{x+4}{3x-2}$ .

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