Question

va rog frumoss dau coroana plus multe puncte

Answer 1

Răspuns

Explicație pas cu pas:

(1/a + 1/(10a + a)) : (1/b + 1/(10b + b))

(1/a + 1/11a) : (1/b + 1/11b)

(11/11a + 1/11a) : (11/11b + 1/11b)

(12/11a) : (12/11b)

12/11a x 11b/12 = b/a

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1/a + 1/aa + 1/aaa = 1/a + 1/11a + 1/111a = 1221/1221a + 111/1221a + 11/1221a = 1343/1221a

1/b + 1/bb + 1/bbb = 1343/1221b

1343/1221a : 1343/1221b = b/a

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1/a - 1/aa + 1/aaa = 1/a - 1/11a + 1/111a = 1221/1221a - 111/1221a + 11/1221a = 1121/1221a

1/b + 1/bb + 1/bbb = 1121/1221b

1121/1221a : 1121/1221b = b/a

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1/ab - 1/abab = 1/(10a + b) - 1 / (1000a + 100b + 10a + b) =

1/(10a + b) - 1/ (1010a + 101b) = (1010a + 101b - 10a -b) / (10a + b)(1010a + 101b) = (1000a + 100b) / (10a + b)(1010a + 101b)

1/ba - 1/baba = 1/(10b + a) -1/(1000b + 100a + 10b + a) = 1/ (10b + a) - 1/(1010b + 101a) = (1010b + 101a - 10b - a) / (10b + a)(1010b + 101a) = (1000b + 100a)/ (10b + a)(1010b + 101a)

(1000a + 100b) / (10a + b)(1010a + 101b) :  (1000b + 100a)/ (10b + a)(1010b + 101a)

ab00/ab*abab : ba00/ba*baba = ab00/ab*abab * ba*baba / ba00 = baba/abab