Question

4." Доведіть тотожність:
Пример на картинке

Answer 1

Объяснение:

$\displaystyle\\1.\\\\\frac{5x}{x-10} +\frac{20x}{x^2-20x+100}=\frac{5x}{x-10} +\frac{20x}{(x-10)^2} =\frac{5x*(x-10)+20x}{(x-10)^2} =\\\\\\=\frac{5x^2-50x+20x}{(x-10)^2} =\frac{5x^2-30x}{(x-10)^2}=\frac{5x*(x-6)}{(x-10)^2} .\\\\2.\\\\\frac{5x*(x-6)}{(x-10)^2}:\frac{4x-24}{x^2-100} =\frac{5x*(x-6)}{(x-10)^2} *\frac{x^2-10^2}{4*(x-6)}=\frac{5x*(x-10)*(x+10)}{4*(x-10)^2}=\\\\ = \frac{5x*(x+10)}{4*(x-10)}=\frac{5x^2+50x}{4*(x-10)} .$

$\displaystyle\\3.\\\\\frac{5x^2+50x}{4*(x-10)} -\frac{25x}{x-10} =\frac{5x^2+50x-4*25x}{4*(x-10)} =\frac{5x^2+50x-100x}{4*(x-10)} =\\\\\\=\frac{5x^2-50x}{4*(x-10)}=\frac{5x*(x-10)}{4*(x-10)}=\frac{5x}{4}.$