Question

If a=1/x+1/y, what is the value of 1/a

Answer 1

To find the value of 1/a, substitute the given expression for a into the expression 1/a. Simplify the resulting expression by finding a common denominator, combining the fractions, and simplifying further. The final value of 1/a is xy/(y + x).

Step-by-step explanation:

To find the value of 1/a, we need to substitute the given expression for a into the expression 1/a. So if a = 1/x + 1/y, then 1/a can be written as:

1. 1/a = 1/(1/x + 1/y)

To simplify this expression, we need to find a common denominator for 1/x and 1/y. The common denominator is xy. So we rewrite 1/x and 1/y with the common denominator:

1. 1/x = y/xy

2. 1/y = x/xy

Now we can substitute these values back into the expression for 1/a:

1. 1/a = 1/(y/xy + x/xy)

Next, we can combine the fractions by adding the numerators:

1. 1/a = 1/((y + x)/xy)

We can simplify this further by multiplying the numerator and denominator by xy:

1. 1/a = xy/(y + x)

   Therefore, the value of 1/a is xy/(y + x).

Answer 2

1/a = xy/(y-x)

Step-by-step explanation:

Simplify the reciprocal:

1/a = 1/(1/x -1/y) = 1/((y-x)/(xy))

1/a = xy/(y-x)