Question

Hello pls someone solve this for me
3/7 + (-6/11) + (-8/21) + 5/22
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Answer 1

`-(125)/(462)`

Explanation:

`(3)/(7) + ( - (6)/(11)) + ( -(8)/(21)) + (5)/(22)\\\\(3)/(7) - (6)/(11) -(8)/(21) + (5)/(22)\\\\((3)/(7) -(8)/(21))+ ((5)/(22) - (6)/(11)) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\ arranging \ the \ terms \ for \ easy \ calculation \ ] \\\\(((3 * 3) - 8)/(21)) + (5 - ( 6 * 2))/(22)\\\\(9-8)/(21) + (5-12)/(22)\\\\(1)/(21) + (-7)/(22)\\\\(1)/(21) - (7)/(22)\\\\((1 * 22) - ( 7 * 21))/(21 *22)\\\\`

`(22-147)/(462)\\\\-(125)/(462)`

Answer 2

Given that 3/7 + (- 6/11) + (- 8/21) + (5/22)

Taking L.C.M. of the denominators 7, 11, 21 and 22 and then solving it.

L.C.M. of 7, 11, 21 and 22 = 2 x 3 x 7 x 11 = 462

= (462/7) x 3 – (462/11) x 6 – (462/21) x 8 + (462/22) x 5

= (198/462) – (252/462) – (176/462) + (105/462)

= (303/462) – (428/462)

= (-125/462)