Write down two unitary fractions whose difference is 1/40
1/20 - 1/40 = 1/40
To find two unitary fractions whose difference is 1/40, we can set up the following equation:
1/x - 1/y = 1/40
To solve this equation, we can use algebraic manipulation.
First, let's clear the fractions by multiplying both sides of the equation by a common denominator. In this case, the common denominator is 40xy:
40y - 40x = xy
Next, let's simplify the equation by moving all the terms to one side:
xy + 40x - 40y = 0
Now, let's factor the equation:
x(y + 40) - 40(y + 40) = 0
Now, let's simplify the equation further by factoring out a common factor:
(x - 40)(y + 40) = 0
Since the product of two numbers is zero if and only if at least one of the numbers is zero, we have two possible solutions:
1. x - 40 = 0, which implies x = 40
Substituting x = 40 into the original equation, we get 1/40 - 1/y = 1/40. This simplifies to 1/y = 0, which does not have a valid solution for y.
2. y + 40 = 0, which implies y = -40
Substituting y = -40 into the original equation, we get 1/x - 1/-40 = 1/40, which simplifies to 1/x + 1/40 = 1/40. By rearranging the terms, we find that 1/x = 0, which does not have a valid solution for x.
Therefore, there are no two unitary fractions whose difference is 1/40.