Ответ:

Пошаговое объяснение:

437. a=1/6

a/(5a-1) ÷a²/(25a²-10a+1)=a/(5a-1) ·(5a-1)²/a²=(5a-1)/a=5 -1/a=5 -1/(1/6)=5-6=-1

438. a=1/7

a/(4a-1) ÷a²/(16a²-8a+1)=a/(4a-1) ·(4a-1)²/a²=(4a-1)/a=4 -1/a=4 -1/(1/7)=4-7=-3

439. a=1/6

a/(9a-1) ÷a²/(81a²-18a+1)=a/(9a-1) ·(9a-1)²/a²=(9a-1)/a=9 -1/a=9 -1/(1/6)=9-6=3

440. a=1/6, b=1/9

b²/(36a²-b²) ÷b/(6a-b)=b²/((6a-b)(6a+b)) ·(6a-b)/b=b/(6a+b)=(1/9)/(6·1/6 +1/9)=(1/9)/(1 1/9)=1/9 ·9/10=1/10=0,1

441. a=4/5, b=4/5

b²/(9a²-4b²) ÷b/(3a-2b)=b²/((3a-2b)(3a+2b)) ·(3a-2b)/b=b/(3a+2b)=(4/5)/(3·4/5 +2·4/5)=(4/5)/((4/5 ·(3+2))=1/5=0,2

442. a=2/3, b=8/9

b²/(16a²-49b²) ÷b/(4a-7b)=b²/((4a-7b)(4a+7b)) ·(4a-7b)/b=b/(4a+7b)=(8/9)/(4·2/3 +7·8/9)=(8/9)/(8/3 +56/9)=(8/9)/(24/9 +56/9)=8/9 ·9/80=1/10=0,1

443. a=5/6, b=5/9

b²/(36a²-b²) ÷b/(6a-b)=b²/((6a-b)(6a+b)) ·(6a-b)/b=b/(6a+b)=(5/9)/(6·5/6 +5/9)=(5/9)/(5 5/9)=5/9 ·9/50=1/10=0,1

444. a=1/15

(a²-25)/(2a²) ·a/(2a-10)=((a-5)(a+5))/(2a·2(a-5))=(a+5)/(4a)=1/4 +5/(4a)=1/4 +5/(4·1/15)=1/4 +5·15/4=(1+75)/4=76/4=19

445. a=1/20

(a²-16)/a² ·a/(a-4)=((a-4)(a+4))/(a(a-4))=(a+4)/a=1 +4/a=1 +4/(1/20)=1+4·20=1+80=81