Simplify r=1/(1/x+1/y)
multiply the right side by xy/xy
To simplify the expression r = 1/(1/x + 1/y), we need to eliminate the fractions in the denominator.
Step 1: Find the common denominator for the fractions 1/x and 1/y. The common denominator is xy.
Step 2: Multiply the numerator and denominator of each fraction by the missing factor to obtain the common denominator xy.
For 1/x, multiply numerator and denominator by y:
1/x * (y/y) = y/xy.
For 1/y, multiply numerator and denominator by x:
1/y * (x/x) = x/xy.
Now, the expression can be rewritten as:
r = 1/(y/xy + x/xy).
Step 3: Combine the fractions with the same denominator:
r = 1/((y + x)/xy).
Step 4: Rewrite the expression by multiplying both numerator and denominator by xy to eliminate the fraction within the fraction:
r = xy/(y + x).
Therefore, the simplified expression is r = xy/(y + x).