Question

4. Докажите тождество: (1/(sqrt(a) + 4) - 1/(4 - sqrt(a))) / ((8sqrt(a))/(2a - 32)) = 0, 5

Answer 1

Ответ:

$\displaystyle \left(\frac{1}{\sqrt{a}+4}-\frac{1}{4-\sqrt{a}}\right):\frac{8\sqrt{a}}{2a-32}=0,5$

Объяснение:

$\displaystyle \left(\frac{1}{\sqrt{a}+4}-\frac{1}{4-\sqrt{a}}\right):\frac{8\sqrt{a}}{2a-32}=\\\\\left(\frac{4-\sqrt{a}}{(4-\sqrt{a})(4+\sqrt{a})}-\frac{4+\sqrt{a}}{(4-\sqrt{a})(4+\sqrt{a})}\right):\frac{8\sqrt{a}}{2(a-16)}=\\\\\left(\frac{4-\sqrt{a}-(4+\sqrt{a})}{16-a}\right):\frac{4\sqrt{a}}{a-16}=\\\\\left(\frac{4-\sqrt{a}-4-\sqrt{a}}{16-a}\right)\cdot \frac{a-16}{4\sqrt{a}}=$

$\displaystyle \left(\frac{-2\sqrt{a}}{16-a}\right)\cdot \frac{-(16-a)}{4\sqrt{a}}=\\\\\left(\frac{-2\sqrt{a}}{16-a}\right)\cdot \frac{-(16-a)}{4\sqrt{a}}=\frac{1}{2}=0,5$