Bonjour je ne comprend pas comment faire l exMerci pour votre réponse .... Pergunta de ideia deyohanclaus2

yohanclaus2 @yohanclaus2

December 2020 1 78 Report

Bonjour je ne comprend pas comment faire l ex

Merci pour votre réponse

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emmmamld122

Bonsoir,

$h = 3 - ( \frac{3}{56} - \frac{3}{24} )$

$h = 3 - ( \frac{3 \times 24}{56 \times 24} - \frac{3 \times 56}{24 \times 56} )$

$h = 3 - ( \frac{72}{1624} - \frac{168}{1624} )$

$h = 3 - ( \frac{72 - 168}{1624} )$

$h = 3 - \frac{ - 96}{1624}$

$h = \frac{3 \times 1624 -( - 96)}{1624}$

$h = \frac{4872 -( - 96)}{1624}$

$h = \frac{4872 + 96}{1624}$

$h = \frac{4968}{1624}$

On va simplifier la fraction en décomposant 4968 et 1624 en nombres premiers.

4968|2

2484|2

1242|2

0621|3

0207|3

0069|3

0023|23

0001

1624|2

0812|2

0406|2

0203|7

0029|29

0001

$h = \frac{4968}{1624} = \frac{2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 23}{2 \times 2 \times 2 \times 7 \times 29}$

$h = \frac{3 \times 3 \times 3 \times 23}{7 \times 29} = \frac{783}{203}$

$h = \frac{4968}{1624} = \frac{783}{203}$

$i = \frac{1}{ \frac{4}{14} + \frac{2}{8} }$

$i = \frac{1}{ \frac{4 \times 8}{14 \times 8} + \frac{2 \times 14}{8 \times 14} }$

$i = \frac{1}{ \frac{32}{112} + \frac{28}{112} }$

$i = \frac{1}{ \frac{32 + 28}{112} }$

$i = \frac{1}{ \frac{60}{112} }$

$i = 1 \times \frac{112}{60} = \frac{112}{60}$

Décomposons 112 et 60 en nombres premiers.

112|2

056|2

028|2

014|2

007|7

001

60|2

30|2

15|3

05|5

01

$i = \frac{112}{60} = \frac{2 \times 2 \times 2 \times 2 \times 7}{2 \times 2 \times 3 \times 5} = \frac{2 \times 2 \times 7}{3 \times 5}$

$i = \frac{28}{15}$

$i = \frac{112}{60} = \frac{28}{15}$

$j = \frac{ \frac{3 }{2} - \frac{5 }{3} }{ \frac{ - 3}{7} + 1}$

$j = \frac{ \frac{3 \times 3}{2 \times 3} - \frac{5 \times 2}{3 \times 2} }{ \frac{ - 3}{7} + \frac{7}{7} }$

$j = \frac{ \frac{9}{6} - \frac{ 10}{6} }{ \frac{ - 3 + 7}{7} }$

$j = \frac{ \frac{9 - 10}{6} }{ \frac{4}{7} }$

$j = \frac{ \frac{ - 1}{6} }{ \frac{4}{7} }$

$j = \frac{ - 1}{6} \times \frac{7}{4}$

$j = \frac{ - 7}{24}$

Bonne nuit !

2 votes Thanks 1

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