How would you set this up? Express the following in its simplest form.

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How would you set this up? Express the following in its simplest form.

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Answer 1 · 2018-01-28T10:03:03

$x - 1$ $x-1$

Explanation:

$to eliminate fractions multiply numerator/denominator$ $"to eliminate fractions multiply numerator/denominator "$
$by x$ $"by x"$

$\Rightarrow \frac{x - \frac{1}{x}}{1 + \frac{1}{x}} \times \frac{x}{x}$ $rArr(x-1/x)/(1+1/x)xx x/x$

$= \frac{x^{2} - 1}{x + 1}$ $=(x^2-1)/(x+1)$

$factorise numerator and cancel common factors$ $"factorise numerator and cancel common factors"$

$x^{2} - 1 is a difference of squares$ $x^2-1" is a "color(blue)"difference of squares"$

$\Rightarrow x^{2} - 1 = (x - 1) (x + 1)$ $rArrx^2-1=(x-1)(x+1)$

$\Rightarrow \frac{x^{2} - 1}{x + 1}$ $rArr(x^2-1)/(x+1)$

$=((x-1)cancel((x+1)))/cancel((x+1))$

$=x-1larr" in the form "Ax+B$

$"with "A=1" and "B=-1$

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How would you set this up? Express the following in its simplest form.

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