Question

7 și 8 va rog foarte frumos

Answer 1

7 ) 4 / 10 = 2 / 5

28 / 84 = ( 28 : 28 ) / ( 84 : 28 ) = 1 / 3

333 / 444 = ( 333 : 111 ) / ( 444 : 111 ) = 3 / 4

25 / 3 250 = ( 25 : 25 ) / ( 3 250 : 25 ) = 1 / 130

( 2 x 5 x 7 ) / ( 3 x 5 x 11 ) = 14 / 33

2³ / 2⁵ = 1 / 2² = 1 / 4

( 5⁴ x 7³ x 11⁴ ) / ( 5⁶ x 7 x 11³ ) = ( 7² x 11 ) / 5² = 539 / 25

( 3 a + 6 b ) / ( 5 a + 10 b ) = 3 ( a + 2 b ) / 5 ( a + 2 b ) = 3 / 5

( 9 a + 3 ) / ( 12 a + 4 ) = 3 ( 3 a + 1 ) / 4 ( 3 a + 1 ) = 3 / 4

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8)

a ) ( 3ⁿ⁺² x 5ⁿ⁺¹ ) / 15ⁿ⁺¹ = ( 3 ⁿ⁺¹ x 3 x 5ⁿ⁺¹ ) / 15ⁿ⁺¹ = ( 3 x 5 )ⁿ⁺¹ x 3 / 15ⁿ⁺¹ = 3

c ) ( 5ⁿ⁺² x 7ⁿ + 5ⁿ x 7ⁿ⁺¹ ) / ( 5ⁿ⁺¹ x 7ⁿ⁺¹ + 7 ⁿ x 5ⁿ⁺² ) =

= 5ⁿ x 7ⁿ x ( 5² + 7 ) / 5ⁿ x 7 ⁿ x ( 5 x 7 + 5² ) =

= ( 25 + 7 ) / ( 35 + 25 ) =

= 32 / 60 =

= 8 / 15

d ) ( 5ⁿ + 5ⁿ⁺¹ + 5 ⁿ⁺² + 5ⁿ⁺³ ) / ( 5ⁿ⁺¹ + 5ⁿ⁺³ ) =

= 5ⁿ ( 1 + 5 + 5² + 5³ ) / 5ⁿ ( 5 + 5³ ) =

1 + 5 + 5² ( 1 + 5 ) = ( 1 + 5 ) ( 1 + 5² ) = ( 1 + 5 ) x 26

5 + 5³ = 5 ( 1 + 5² ) = 5 x 26

= ( 1 + 5 ) x 26 / 5 x 26 =

= ( 1 + 5 ) / 5