Simplify 1/r=1/x+1/y
Multiply both sides by rxy. Then simplify. I will be happy to check your work.
That is as compact and simple as the relationship can be written. Are you looking for an explicit formula for x, y or r?
To simplify the equation 1/r = 1/x + 1/y, you can start by multiplying both sides of the equation by rxy:
(rxy) * (1/r) = (rxy) * (1/x + 1/y)
The left-hand side simplifies to xy, and the right-hand side simplifies to r(x + y):
xy = r(x + y)
Now, if you would like to solve for x explicitly, you can start by rearranging the equation:
xy = rx + ry
Move the r terms to one side:
xy - rx - ry = 0
Factor out x and y:
x(y - r) - ry = 0
Now, isolate x:
x(y - r) = ry
Divide both sides by (y - r):
x = ry / (y - r)
If you want to solve for y explicitly, you can rearrange the equation in a similar way:
xy = rx + ry
Move the x terms to one side:
xy - rx - ry = 0
Factor out y:
y(x - r) - rx = 0
Isolate y:
y(x - r) = rx
Divide both sides by (x - r):
y = rx / (x - r)
I hope this helps! Let me know if you have any further questions.
To simplify the equation 1/r = 1/x + 1/y, you can follow these steps:
Step 1: Start with the equation 1/r = 1/x + 1/y.
Step 2: Multiply both sides of the equation by rxy to eliminate the denominators:
rxy * (1/r) = rxy * (1/x + 1/y).
This simplifies to:
xy = ry + rx.
Step 3: Distribute rxy on the right side of the equation:
xy = rxy/x + rxy/y.
Step 4: Simplify the equation by dividing both sides by xy:
xy/(xy) = (rxy/x + rxy/y)/(xy).
This simplifies to:
1 = (r*y + r*x)/(xy).
Alternatively, you can express it as an explicit formula for r:
r = (xy)/(x + y).
For a specific value of x and y, you can substitute those values into the formula to find the corresponding value of r.
Now, you can check if our work is correct by substituting actual values for x, y, and r, and comparing both sides of the equation.