Question 1090933
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Solve: (1-x)/(2+x) = (x-2)/(x+1)
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<pre>
{{{(1-x)/(2+x)}}} = {{{(x-2)/(x+1)}}}.


Cross-multiply:


(1-x)*(x+1) = (x-2)*(2+x),

(1-x)*(1+x) = (x-2)*(x+2),

{{{1-x^2}}} = {{{x^2-4}}},

{{{2x^2}}} = 5  ====>  {{{x^2}}} = {{{5/2}}}  ====>  x = +/- {{{sqrt(5/2)}}} = +/- {{{sqrt(10)/2}}}.


<U>Answer</U>.  x = +/- {{{sqrt(10)/2)}}}.
</pre>

Solved.