Question

x+y^-1 * (x^-1 + y^-1) = 1 / xy

prove!

Answer 1

Given :-

• (x + y⁻¹) (x⁻¹ + y⁻¹)

To prove :-

• (x + y⁻¹) (x⁻¹ + y⁻¹) = 1/xy

Solution :-

• (x + y⁻¹) (x⁻¹ + y⁻¹)

★  (x + y⁻¹) can be written as 1/x+y       (Reciprocal) (a⁻¹ = 1/a)

★  (x⁻¹ + y⁻¹) can be written as 1/x+1/y  (Reciprocal) (a⁻¹ = 1/a)

• 1/x+y [y+x/xy]              ( x + y and y + x get cancelled)
• 1/xy

∴  (x + y⁻¹) (x⁻¹ + y⁻¹) = 1/xy