Question 187889
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{\frac{2}{x+5}}{\frac{4}{x^2-25}}]


Remember, invert and multiply:



*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \left(\frac{2}{x+5}\right)\left(\frac{x^2-25}{4}\right)]


Notice that the right-hand fraction has the difference of two squares in the numerator, so factor it:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \left(\frac{2}{x+5}\right)\left(\frac{(x+5)(x-5)}{4}\right)]


Eliminate factors common to both numerator and denominator:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \left(\frac{1}{1}\right)\left(\frac{x-5}{2}\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  \frac{x-5}{2}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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