One number is 5 times another. Write an expression for the sum of their reciprocals. Then simplify the expression. (Use x for the variable.)
The numbers: x and x/5
The reciprocals: 1/x and 5/x
The sum of the reciprocals: 6/x
Let's denote one number as x and the other number as 5x, since it is stated that one number is 5 times another.
Now, let's write an expression for the sum of their reciprocals. The reciprocal of a number is found by dividing 1 by the number itself. So, the reciprocal of x is 1/x, and the reciprocal of 5x is 1/(5x).
The sum of their reciprocals can be written as:
(1/x) + (1/(5x))
To simplify this expression, we need a common denominator, which in this case is 5x.
To achieve that, let's multiply the first fraction by (5/5) and the second fraction by (1/x):
(1/x) + (1/(5x)) = (5/5x) + (1/(5x))
Now, we can combine the fractions:
(5/5x) + (1/(5x)) = (5 + 1)/(5x) = (6)/(5x)
Therefore, the simplified expression for the sum of the reciprocals of the two numbers is 6/(5x).