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For what value of x will (3 + x)/(5 + x) and (1 - x)/(2 + x) be equal?

 Feb 18, 2021
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Cross multiply and simplify:\(\frac{3+x}{5+x} = \frac{1-x}{2+x}\)

\((3+x)(2+x) = (1-x)(5+x)\)

 

\(x^2 + 5x + 6 = -x^2 - 4x + 5\)

 

So, \(x = -\frac{9}{4} \pm \frac{\sqrt{73}}{4}\)

 Feb 19, 2021

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