Question

4/x-y + 1/ x+y =3 ; 2/x-y - 3/x+y =5​

Answer 1

Step-by-step explanation:

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Answer 2

The given equation is

$\frac{4}{x - y} + \frac{1}{x + y} = 3 \\ \frac{2}{x - y} - \frac{3}{ x + y} = 5$

let x-y=m band x+y=n

$\frac{4}{m} + \frac{1}{n} = 3 \\ \frac{2}{m} - \frac{3}{n} = 5$

4n+m=3mn ---- 1

2n-3m=5mn ----2

multiply 2 by 2 we get,

4n-6m=10 mn. -------3

subtract 1 and 3 we get

$4n - 6m = 10mn \\ ( - ) 4n + m = 3mn \\ 0 - 7m = 7mn$

Therefore

$n = \frac{ - 7m}{7m} = - 1$

sub n=-1 in 1 we get

$4( - 1) + m = 3m( - 1) \\ - 4 + m = - 3m \\ - 4 = - 3m - m \\ - 4 = - 4m \\ m = \frac{ - 4}{ - 4 } \\ m = 1$

here m=1 and n=-1

which is x-y= 1 and x+y= -1

on solving these two we get,

$x - y = 1 \\ ( + )x + y = - 1 \\ 2x = 0 \\ x = 0 \\ 0 + y = - 1 \\ = - 1$

Therefore the final answer is x=0 and y=-1.

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