Question

prove that 1/x + 1/y =1/2​

Answer 1

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!

To solve for either x or y, the first step is to clear the fractions by multiplying both sides by the LCD which is 2xy

1/x+1/y=1/2

2xy(1/x)+2xy(1/y)=2xy(1/2)

2y+2x=xy

Now, to solve for x, get all the x terms on one side by subtracting 2x from each side:

2y=xy-2x

Factor the x, so as to get the x's all in one place:

2y=x(y-2)

Divide both sides by (y-2):

2y/y-2=x(y-2)/y-2

2y/y-2=x

NOW, to solve for y in terms of x, go back to the equation 2y+2x=xy

To solve for y, get all the y terms on one side by subtracting 2y from each side:

2x=xy-2y

Factor the y, so as to get the y's all in one place:

2x=y(x-2)

Divide both sides by (x-2):

2x/x-2=y(x-2)/x-2

2x/x-2=y

R^2 at SCC