SOLUTION: M = 1/ 1/x + 1/y what is x equal to in this equation?

Question 1038724: M = 1/ 1/x + 1/y what is x equal to in this equation?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
It depends
1/(1/x)+ (1/y)=M
x+(1/y)=M
xy+1=My, multiplying by y
xy=My-1
x=(My-1)/y
Let x=2 and y=4
1(1/2)+(1/4)=9/4
2 should equal [(9/4)*4]-1/4, and that is (9-1)/4=2
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Other way this can be interpreted is M=1/((1/x)+(1/y))
M=xy/(y+x), making a common denominator of xy in the denominator and putting y+x over it, then inverting, since it is 1 divided by all of that.
My+Mx=xy
My=xy-Mx
My=x(y-M)
x=My/(y-M)
x=2 y=4 1/((1/2)+(1/4))=4/3
2=4M/(4-M)
8-2M=4M
8=6M
M=(4/3)

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