If x =4ab/a+b find x+2a/x-2a + x+2b/x-2b

Question

If x =4ab/a+b find x+2a/x-2a + x+2b/x-2b

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Caroline 3 weeks 2021-10-05T06:10:09+00:00 1 Answer 0 views 0

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    2021-10-05T06:11:12+00:00

    Answer:

    (x+2a)/(x-2a) + (x+2b)/(x-2b)=2

    Step-by-step explanation:

    Given  

    x=4ab/a+b

    We need to find for x+2a/x-2a + x+2b/x-2b

    Follow the below steps to find the solution.

    Step 1:

    x=4ab / a+ b

    Simplify as

    =>x=2a x 2b / a + b

    =>x/2a=2b / a + b

    By componendo dividend,

    (x+2a)/(x-2a)=(2b+a+b)/(2b-a-b)

    Simplify RHS.

    (x+2a)/(x-2a)=(a+3b)/(b-a)

    Step 2:

    Similarly (x+2b)/(x-2b)=(3a+b)/(a- b)

    Now we know:

    (x+2a) / (x-2a) + (x+2b)/(x-2b)

    =(a+3b)/(b-a) + (3a+b)/(a- b)

    =(a+3b)/(b-a) – (3a+b)/(a- b)

    =a+3b-3a-b/b-a

    =2b-2a/b-a

    =2(b-a)/b-a

    =2

    Finally we get, (x+2a)/(x-2a) + (x+2b)/(x-2b)=2

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