Question

If p = 4xy / (x+y) , prove that
(p + 2x / p - 2x ) + (p + 2y / p - 2y) = 2

plz answer ASAP (,╯︵╰,)

Answer 1

Here we have: p = 4xy/(x+y) which will imply that p/2x = 2y/(x+y). In other words we can say that:

(p+2x)/(p-2x) = (2y + x + y)/(2y – (x + y))              [By componendo and dividendo]

(p +  2x)/(p-2x) = (3y + x)/(y – x)            ….. (i)

Again, we can say that p = 4xy/(x+y)    and we can say that p/2y = 2x/(x + y)

Also, this means thta (p + 2y)/(p – 2y) = (2x + x + y)/(2x – (x +y))          [By componendo and dividendo]

Therefore, we have: (p + 2y)/(p – 2y) = (3x + y)/(x – y) ….(ii)

Adding (i) and (ii), we get:

(p + 2x)/(p – 2x) + (p + 2y)/(p – 2y) = (3y + x)/(y – x) + (3x + y)/(x – y)

In other words, this can be written as: (3y + x)/(y -x) – (3x + y)/(y – x) = (3y + x – 3x – y)/(y -x) = (2y – 2x)/(y – x)

Hence, we have: 2(y – x)/(y – x) = 2. 
HENCE PROVED

Answer 2

hope it may help u