+0

0
317
1
+2448

Simplify

Nov 14, 2018

#1
+8756
+3

$$\ \phantom{=}\,\dfrac{\frac{u+4}{25}-\frac{u+4}{5}}{\frac{4}{u+4}}\\~\\ =\,(\frac{u+4}{25}-\frac{u+4}{5})\div\frac{4}{u+4}\\~\\ =\,(\frac{u+4}{25}-\frac{u+4}{5})\cdot\frac{u+4}{4}\\~\\ =\,(\frac{u+4}{25}-\frac{u+4}{5}\cdot\frac55)\cdot\frac{u+4}{4}\\~\\ =\,(\frac{u+4}{25}-\frac{5(u+4)}{25})\cdot\frac{u+4}{4}\\~\\ =\,(\frac{1(u+4)-5(u+4)}{25})\cdot\frac{u+4}{4}\\~\\ =\,(\frac{-4(u+4)}{25})\cdot\frac{u+4}{4}\\~\\ =\,\frac{-4(u+4)(u+4)}{4(25)}\\~\\ =\,\frac{-(u+4)(u+4)}{25}\\~\\ =\,\frac{-(u+4)^2}{25}$$

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Nov 14, 2018

$$\ \phantom{=}\,\dfrac{\frac{u+4}{25}-\frac{u+4}{5}}{\frac{4}{u+4}}\\~\\ =\,(\frac{u+4}{25}-\frac{u+4}{5})\div\frac{4}{u+4}\\~\\ =\,(\frac{u+4}{25}-\frac{u+4}{5})\cdot\frac{u+4}{4}\\~\\ =\,(\frac{u+4}{25}-\frac{u+4}{5}\cdot\frac55)\cdot\frac{u+4}{4}\\~\\ =\,(\frac{u+4}{25}-\frac{5(u+4)}{25})\cdot\frac{u+4}{4}\\~\\ =\,(\frac{1(u+4)-5(u+4)}{25})\cdot\frac{u+4}{4}\\~\\ =\,(\frac{-4(u+4)}{25})\cdot\frac{u+4}{4}\\~\\ =\,\frac{-4(u+4)(u+4)}{4(25)}\\~\\ =\,\frac{-(u+4)(u+4)}{25}\\~\\ =\,\frac{-(u+4)^2}{25}$$