What is ((a-b))/(a^2-2ab+b^2)-3/(a-b)=a+b ?

The solution to ((a-b))/(a^2-2ab+b^2)-3/(a-b)=a+b is Hyperbola with (h,k)=(0,0),a=sqrt(2),b=sqrt(2)

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((a-b))/(a^2-2ab+b^2)-3/(a-b)=a+b

\frac{( a - b )}{a ^{2} - 2 ab + b ^{2}} - \frac{3}{a - b} = a + b

(h, k) = (0, 0), a = 2, b = 2

Solution steps

\frac{a - b}{a ^{2} - 2 ab + b ^{2}} - \frac{3}{a - b} = a + b

Rewrite

\frac{a - b}{a ^{2} - 2 ab + b ^{2}} - \frac{3}{a - b} - a - b = 0

in the form of a standard hyperbola equation

\frac{( b - 0 ) ^{2}}{( 2 ) ^{2}} - \frac{( a - 0 ) ^{2}}{( 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = 2, b = 2

9 (X^{2} + 6 X) - 4 Y^{2} = - 45

4 y^{2} - x^{2} + 2 x + 16 y + 7 = 0

(x - 3) (x + 1) = yy

x^{2} - 25 y^{2} = 25

x^{2} + 6 x - 4 y^{2} - 8 y + 9 = 0

What is ((a-b))/(a^2-2ab+b^2)-3/(a-b)=a+b ?
The solution to ((a-b))/(a^2-2ab+b^2)-3/(a-b)=a+b is Hyperbola with (h,k)=(0,0),a=sqrt(2),b=sqrt(2)