Question

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

Answer 1

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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