Question

If x = `(5ab)/(a − b), a ≠ b,`

1. Find: `x/a`
2. Using properties of proportion, find: `(x + a)/(x - a)`

Answer 1

(a) Given: x = `(5ab)/(a − b)`

Multiplying `1/a` on both sides of the equation:

⇒ `x/a = 1/a((5ab)/(a - b))`

⇒ `x/a = (5b)/(a - b)`

(b) Since,

⇒ `x/a = (5b)/(a - b)`

Applying componendo and dividendo, we get:

⇒ `(x + a)/(x - a) = (5b + (a - b))/(5b - (a - b))`

⇒ `(x + a)/(x - a) = (5b + a - b)/(5b - a + b)`

⇒ `(x + a)/(x - a) = (a + 4b)/(6b - a)`