Question

find the sum of
$\frac{1}{1 - x} + \frac{ {x}^{2} }{x - 1}$
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Answer 1

Answer:

$Let's multiply</p><p></p><p>x−1/x−−−−−−√+1−1/x−−−−−−√=x(1)(1)x−1/x+1−1/x=x</p><p></p><p>by (x−1/x−−−−−−√−1−1/x−−−−−−√)(x−1/x−1−1/x). Then we get</p><p></p><p>x−1=x(x−1/x−−−−−−√−1−1/x−−−−−−√)x−1=x(x−1/x−1−1/x)</p><p></p><p>x−1/x−−−−−−√−1−1/x−−−−−−√=1−1/x(2)(2)x−1/x−1−1/x=1−1/x</p><p></p><p>Sum up (1)(1) and (2)(2) to get</p><p></p><p>2x−1/x−−−−−−√=x−1/x+12x−1/x=x−1/x+1</p><p></p><p>Now make the substitution y=x−1/x−−−−−−√y=x−1/x. The rest is clear.$

Step-by-step explanation:

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