SOLUTION: Can you help me find what "w" is in this equation 1/x+1/w=1/y I understand to multiply by the least common denominator but I am lost after that. Thanks

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you help me find what "w" is in this equation 1/x+1/w=1/y I understand to multiply by the least common denominator but I am lost after that. Thanks      Log On


   

Question 655628: Can you help me find what "w" is in this equation
1/x+1/w=1/y
I understand to multiply by the least common denominator but I am lost after that.
Thanks
Found 3 solutions by MathDazed, Alan3354, fcabanski:
Answer by MathDazed(34) About Me  (Show Source):
You can put this solution on YOUR website!
1/x + 1/w = 1/y
Find the LCM which is xwy
{(wy + xy = xw)/xwy}
Since you have an equation over the LCM, you can disregard the LCM
wy + xy = xw
Collect like terms
wy - xw = -xy
Factor out w
w(y-x) = -xy
Divide both sides by (y-x)
w = -xy/(y-x)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/x+1/w=1/y
1/w = 1/y - 1/x = (x-y)/xy
Invert
w = xy/(x-y)

Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
1. Combine the fractions using an LCD: (w+x)/xw = 1/y


2. Cross multiply: yw+yx = xw


3. Move the w terms to the same side: yx = xw - yw


4. Remove w from all terms on the right: yx = w(x-y)


5. Divide both sides by x-y: yx/(x-y) = w