Question

4/x-5/y=x+y/xy+3/10 3xy=10(y-x)​

Answer 1

Equation (1)  4/x - 5/y = (x+y)/ xy + 3/10

Taking L.C.M

(4y-5x)/ xy = (10x+10y+3xy) / 10xy

Cancelling both the 'xy's in the denominators

4y-5x = (10x+10y+3xy)/10

Cross multiplying, we get

40y-50x = 10x+10y+3xy

10x+10y+3xy-40y+50x=0

60x-30y+3xy=0....................... equation (1)

Equation (2)  

  3xy= 10(y-x)

3xy=10y-10x

-10x+10y-3xy = 0 .................. equation (2)

Solving both the following simplified equations

 60x-30y+3xy =0...............(a)

-10x+10y -3xy = 0..............(b)

(a) + (b)  

50x - 20y = 0

50x = 20y

x/y = 20/50

x : y :: 2:5

x=2 & y=5