Question

Представьте в виде рациональной дроби​

Answer 1

$1. \frac{3}{a-\frac{1}{b} } = \frac{3b}{ab-1}$

$2. x + \frac{2}{y + \frac{2}{z} } = \frac{xyz+2x+2z}{yz+2}$

$3. \frac{1}{1 - \frac{1}{1-\frac{1}{a} } } = - a + 1$

$4. \frac{a-\frac{ab}{b-c} }{b-\frac{ab}{a-c} } = \frac{a^{2}-ac }{b^{2} -bc}$

$5. 2*\frac{a+1}{a-1} - \frac{1+\frac{1}{a} }{1-\frac{1}{a} }= \frac{a+1}{a-1}$

$6. \frac{a+b - \frac{4ab}{a+b} }{\frac{1}{a-b} + \frac{a-b}{4ab} } = \frac{4a^{4}b-12a^{3}b^{2} + 12a^{2}b^{3} -4ab^{4}}{3a^{2}b+a^{3} +3ab^{2}+b^{3} }$

Answer 2

Смотри ниже.

Пошаговое объяснение:

$1) \frac{3}{a-\frac{1}{b} } =\frac{3}{\frac{ab-1}{b}} =\frac{3b}{ab-1}$

$2) x+\frac{2}{y+\frac{2}{z} } =x+\frac{2}{\frac{yz+2}{z}} =x+\frac{2z}{yz-2}=\frac{x*(yz-2)+2z}{yz-2} = \frac{xyz-2x+2z}{yz-2}$

$3) \frac{1}{1-\frac{1}{1-\frac{1}{a} } } =\frac{1}{1-\frac{1}{\frac{a-1}{a} } }=\frac{1}{\frac{a-1-a}{a-1}} =\frac{a-1}{-1} =1-a$

$4) \frac{a-\frac{ab}{b-c} }{b-\frac{ab}{a-c} } =\frac{\frac{ab-ac-ab}{b-c} }{\frac{ab-bc-ab}{a-c} } =\frac{-ac(a-c)}{-bc(b-c)}=\frac{a^{2}-ac}{b^{2}-bc }$

$5) 2\frac{a+1}{a-1} -\frac{1+\frac{1}{a} }{1-\frac{1}{a} } =\frac{2(a+1)}{a-1}-\frac{\frac{a+1}{a} }{\frac{a-1}{a} } =\frac{2(a+1)}{a-1}-\frac{a+1}{a-1}=\frac{2(a+1)-(a+1)}{a-1} =\frac{a+1}{a-1}$

$6) \frac{a+b-\frac{4ab}{a+b} }{\frac{1}{a-b}+\frac{a-b}{4ab} } =\frac{\frac{(a+b)^{2} -4ab}{a+b} }{\frac{4ab+(a-b)^{2} }{4ab(a-b)} } =\frac{((a+b)^{2} -4ab)4ab(a-b)}{(a+b)(4ab+(a-b)^{2})}$