Evaluate: x+y/xy if x=1/8 and y=1/3
Find common denominator.
1/8 + 1/3 = 3/24 + 8/24 = 11/24
1/8 * 1/3 = 1/24
11/24 divided by 1/24 = 11/24 * 24/1 = ?
To evaluate the expression x + y/xy with the given values of x and y, we substitute the values and simplify the expression.
Step 1: Substitute the values of x and y into the expression.
x + y/xy = (1/8) + (1/3) / (1/8 * 1/3)
Step 2: Simplify the expression inside the parentheses.
= (1/8) + (1/3) / (1/24)
Step 3: Simplify the expression inside the division.
= (1/8) + (1/72)
Step 4: Find a common denominator for the fractions.
The common denominator of 8 and 72 is 72.
= (9/72) + (1/72)
Step 5: Simplify the expression by combining the fractions.
= 10/72
Step 6: Reduce the fraction to its simplest form.
The greatest common divisor of 10 and 72 is 2.
= 5/36
Therefore, the value of x + y/xy when x = 1/8 and y = 1/3 is 5/36.