Question

1/x+1/y+1/z = 1, Find the values of x, y and z.

Answer 1

Answer:

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Step-by-step explanation:

1/x + 1/y = 1/z

 

z(1/x + 1/y) = z/z = 1

 

z(1/x + 1/y)/(1/x + 1/y) = z = 1/(1/x + 1/y)

 

so z +1 = 1/(1/x + 1/y) + 1

 

you can make it slightly prettier by simplifying terms as follows

 

z = 1/(1/x + 1/y)

z = 1/(1/x(y/y) + 1/y(x/x))

z = 1/(y/xy + x/xy)

z = 1/((y+x)/xy)

z = xy/(y+x)

 

so you get z + 1 = xy/(y+x) + 1.

 

You can represent the 1 as x and y as follow

 

z + 1 = xy/(y+x) + 1

z + 1 = xy(y+x) + 1(y+x)/(y+x)

z + 1 = xy(y+x) + (y+x)/(y+x)

z + 1 = (xy + y + x)/(y+x)