Question

x+2a/x-2a + x+2b/x-2b=?if x=4ab/a+b then

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

Answer 2

Answer: x = 4ab/(a+b)

x+2a/ x-2a + x+2b/x-2b

= [ 4ab/ (a+b) +2a] / [ 4ab/ ( a+b) -2a] + [ 4ab/(a+b) +2b ] / [ 4ab/ (a+b) - 2b]

= [4ab + 2a^2 +2ab]/ [4ab- 2a^2 - 2ab]

+ [ 4ab+2b^2 +2ab] / [4ab - 2b^2 - 2ab]

= [6ab + 2a^2]/ [2ab- 2a^2 ] + [6ab + 2b^2 ] / [2ab - 2b^2]

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

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

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

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

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

=2

Step-by-step explanation: