What is y 1/x+1/(x+y)=1 ?

The solution to y 1/x+1/(x+y)=1 is Hyperbola with (h,k)=(1/2 ,0),a= 1/2 ,b= 1/2

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

y \frac{1}{x} + \frac{1}{x + y} = 1

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{1}{2}

Solution steps

y \frac{1}{x} + \frac{1}{x + y} = 1

Rewrite

y \frac{1}{x} + \frac{1}{x + y} = 1

in the form of a standard hyperbola equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{1}{2} ) ^{2}} - \frac{( y - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{1}{2}, 0), a = \frac{1}{2}, b = \frac{1}{2}

4 y^{2} + 2 y = x^{2} - 1

9 x^{2} - 4 y^{2} - 18 x - 24 y - 63 = 0

9 x^{2} - 4 y^{2} + 54 x - 8 y + 78 = 0

4 x^{2} - 9 y^{2} + 36 = 0

8 x^{2} - 3 y^{2} = 120

What is y 1/x+1/(x+y)=1 ?
The solution to y 1/x+1/(x+y)=1 is Hyperbola with (h,k)=(1/2 ,0),a= 1/2 ,b= 1/2