Освобождения от иррациональности в знаменателе дроби1) ( x+y)/(x-y) 2)

1) (x+y)/(x-y)=

= (x+y)/[(x-y)( x+y)] =

= (x+y)/[(x)-(y)] =

= (x+y)/(x-y)

2) (20-4a)/(5a-a) =

= 4(5 - a)/(5а - aa)

= 4(5 - a)/[a(5 -a)] =

= 4/a =

= 4a/(aa) =

= 4a/a

3) (9a+b)/(9b+81ab) =

= (9a+b)/[9b(b+9a]) =

= 1/(9b) =

= b/(9b)

4) (x-ax)/(ax-aa) =

= x(x - a)/[a(x - a)] =

= x/a =

= (ax)/a

1) 

(\sqrtx-\sqrty)/(\sqrtx+\sqrty)=
(\sqrtx-\sqrty)(\sqrtx-\sqrty)/(\sqrtx+\sqrty)(\sqrtx-\sqrty)=
(x-2\sqrtxy+y)/(x-y)

2) 

(20-4\sqrta)/(5\sqrta-a)=4(5-\sqrta)/\sqrta(5-\sqrta)=4\sqrta/a

3)

(9\sqrta+\sqrtb)/(9b+81\sqrtab)=(9\sqrta+\sqrtb)/(9\sqrtb(\sqrtb+9\sqrta)=\sqrtb/9b

4) 

(x-a\sqrtx)/(\sqrtax-a\sqrta)=\sqrtx(\sqrtx-a)/\sqrta(\sqrtx-a)=\sqrtax/a