Find f(g(x)) f(x)=2/(x-7) , g(x)=2/x+7

$f (x) = \frac{2}{x - 7}$ , $g (x) = \frac{2}{x} + 7$

Set up the composite result function.

$f (g (x))$

Evaluate $f (g (x))$ by substituting in the value of $g$ into $f$ .

$f (\frac{2}{x} + 7) = \frac{2}{(\frac{2}{x} + 7) - 7}$

Simplify the denominator.

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Subtract $7$ from $7$ .

$f (\frac{2}{x} + 7) = \frac{2}{\frac{2}{x} + 0}$

Add $\frac{2}{x}$ and $0$ .

$f (\frac{2}{x} + 7) = \frac{2}{\frac{2}{x}}$

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{2}{x} + 7) = 2 (\frac{x}{2})$

Cancel the common factor of $2$ .

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Cancel the common factor.

$f (\frac{2}{x} + 7) = 2 (\frac{x}{2})$

Rewrite the expression.

$f (\frac{2}{x} + 7) = x$

Find f(g(x)) f(x)=2/(x-7) , g(x)=2/x+7

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