Question

3/x+y-4/x-y=5;4/x+y-4/x-y=6

Answer 1

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Answer 2

Solution :-

Q: [3/(x + y)] - [4/(x - y)] = 5 ______(i)

[4/(x + y)] - [4/(x - y)] = 6 _______(ii)

Let 1/(x + y) = A

1/(x - y) = B

So, 3A - 4B = 5 ______(iii)

4A - 4B = 6 ______(iv)

On Subtracting equation (iii) from (iv) we get,

(4A - 4B) - (3A - 4B) = 6 - 5

=> 4A - 4B - 3A + 4B = 1

=> A = 1

Putting the value of A in equation (iii),

3 × 1 - 4B = 5

=> - 4B = 5 - 3

=> - 4B = 2

=> B = 2/-4 = - 1/2

Now,

1/(x + y) = A = 1

=> x + y = 1

=> x = 1 - y _____(v)

1/(x - y) = B = - 1/2

=> x - y = - 2

=> 1 - y - y = - 2 [from equation (v)]

=> - 2y = - 2 - 1

=> y = - 3/-2 = 3/2

Putting the value of y in equation (v),

x = 1 - 3/2

=> x = (2 - 3)/2 = - 1/2

Hence,

x = - 1/2

y = 3/2