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# algebra

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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