What is 2/(x-y)+3/(x+y)=2 ?

The solution to 2/(x-y)+3/(x+y)=2 is Hyperbola with (h,k)=(5/4 , 1/4),a=sqrt(3/2),b=sqrt(3/2)

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2/(x-y)+3/(x+y)=2

\frac{2}{x - y} + \frac{3}{x + y} = 2

(h, k) = (\frac{5}{4}, \frac{1}{4}), a = \frac{3}{2}, b = \frac{3}{2}

Solution steps

\frac{2}{x - y} + \frac{3}{x + y} = 2

Rewrite

\frac{2}{x - y} + \frac{3}{x + y} = 2

in the form of a standard hyperbola equation

\frac{( x - \frac{5}{4} ) ^{2}}{( \frac{3}{2} ) ^{2}} - \frac{( y - \frac{1}{4} ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{5}{4}, \frac{1}{4}), a = \frac{3}{2}, b = \frac{3}{2}

y^{2} - x^{2} = 27

(x + y) (x - y) = 14

(x + y) (x - y) = 12

(\frac{y - 4}{9})^{2} - (\frac{x - 6}{5})^{2} = 1

3 y^{2} - 4 x^{2} - 8 x - 24 y - 40 = 0

What is 2/(x-y)+3/(x+y)=2 ?
The solution to 2/(x-y)+3/(x+y)=2 is Hyperbola with (h,k)=(5/4 , 1/4),a=sqrt(3/2),b=sqrt(3/2)