What is the answer to solvefor y,x^2=(x+2y)/(x-2y) ?

The answer to solvefor y,x^2=(x+2y)/(x-2y) is y=-(x-x^3)/(2(x^2+1));\quad x\ne i,x\ne-i

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solvefor y,x^2=(x+2y)/(x-2y)

solve for

y, x^{2} = \frac{x + 2 y}{x - 2 y}

y = - \frac{x - x ^{3}}{2 ( x ^{2} + 1 )}; x \neq = i, x \neq = - i

Solution steps

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

Multiply both sides by

x - 2 y

x^{2} (x - 2 y) = x + 2 y

Expand

x^{2} (x - 2 y) : x^{3} - 2 y x^{2}

x^{3} - 2 y x^{2} = x + 2 y

Move

x^{3}

to the right side

- 2 y x^{2} = x + 2 y - x^{3}

Move

2 y

to the left side

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

Factor

- 2 y x^{2} - 2 y : - 2 y (x^{2} + 1)

- 2 y (x^{2} + 1) = x - x^{3}

Divide both sides by

- 2 (x^{2} + 1); x \neq = i, x \neq = - i

y = - \frac{x - x ^{3}}{2 ( x ^{2} + 1 )}; x \neq = i, x \neq = - i

t, \frac{h}{g} = \frac{4 R}{t}

t, y = \frac{2 t}{t - 1}

\frac{8}{x - 3} = \frac{6}{15}

y, x = \frac{km}{y - p}

\frac{3}{x - 2} = \frac{8}{x + 6}

What is the answer to solvefor y,x^2=(x+2y)/(x-2y) ?
The answer to solvefor y,x^2=(x+2y)/(x-2y) is y=-(x-x^3)/(2(x^2+1));\quad x\ne i,x\ne-i