Dear Student , Please find below the solution to the asked query : 3 a+bx+y - 2 a-bx-y =18 a+bx+y + 7 b-ax-y =1Put 1x+y = u and 1x-y=v3 a+b u - 2 a-b v =1 i8 a+b u + 7 b-a v =1 iiMultiplying eqn i by 8 and eqn ii by 3 and then subracting eqn i from ii24 a+b u + 21 b-a v - 24 a+b u + 16 a-b v = 3 - 8 21 b-a v - 16 b-a v = -55 b-a v=-5v = -1b-aSubstituing the value of v in eqn ii , we get8 a+b u + 7 b-a -1b-a=18 a+b u -7=18 a+b u = 8u = 1a+bNow,1x+y=1a+bx+y=a+b iiiand1x-y=-1b-ax-y = a-b ivAdding eqn iii and eqn iv2x=2ax=aanda+y=a+by=b Hope this information will clear your doubts about the topic If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible Regards

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Please find below the solution to the asked query :

\frac{3 (a + b)}{x + y} - \frac{2 (a - b)}{x - y} = 1 \frac{8 (a + b)}{x + y} + \frac{7 (b - a)}{x - y} = 1 Put \frac{1}{x + y} = u and \frac{1}{x - y} = v 3 (a + b) u - 2 (a - b) v = 1 . . . (i) 8 (a + b) u + 7 (b - a) v = 1 . . . (ii) Multiplying eqn (i) by 8 and eqn (ii) by 3 and then subracting eqn (i) from (ii) 24 (a + b) u + 21 (b - a) v - 24 (a + b) u + 16 (a - b) v = 3 - 8 21 (b - a) v - 16 (b - a) v = - 5 5 (b - a) v = - 5 v = \frac{- 1}{b - a} Substituing the value of v in eqn (ii), we get 8 (a + b) u + 7 (b - a) (\frac{- 1}{b - a}) = 1 8 (a + b) u - 7 = 1 8 (a + b) u = 8 u = \frac{1}{a + b} Now, \frac{1}{x + y} = \frac{1}{a + b} x + y = a + b . . . (iii) and \frac{1}{x - y} = \frac{- 1}{b - a} x - y = a - b . . . (iv) Adding eqn (iii) and eqn (iv) 2 x = 2 a x = a and a + y = a + b y = b .

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