Question

Solve 1∕(x+y) + 2/(x-y)= 1/15

1/3(x+2y) - 1/3(x-2y)=-8/45

Answer 1

Answer:

Step-by-step explanation:

1. let 1/(x+y) be m and 1/(x-y) be n

therefore m + 2n = 1/15                eqn1

2. let 1/(3x +2y) be m and 1/ (3x - 2y) be n

therefore m-n = - 8/45       eqn 2

3. (m + 2n ) 15 =1   :   15m + 30n = 1     eqn3                * 3

4. (m-n) 45 = -8     :   45m - 45n = -8    eqn4

5. now  multiply eqn 1 by 3

we get 45m + 90n = 3           eqn 5

6. add the eqns 4 and 5  

7.                 45m + 90n = 3

                   45m - 45n = -8

                     0    + 45n = -5

8.      45n = -5

 n = - 5 / 45

n= - 1/9

substitues in eqn 1

m + 2n = 1/ 15

m + 2 * (- 1/9) = 1/15

m - 2/9 = 1/15

m = 1/15 + 2/9

m = 3/45 + 10/45

m = (3 + 10 ) /45

m= 13/ 45