What is the answer to solvefor y,f=-(40000x)/((3+x^2+2y^2)^2) ?

The answer to solvefor y,f=-(40000x)/((3+x^2+2y^2)^2) is

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solvefor y,f=-(40000x)/((3+x^2+2y^2)^2)

solve for

y, f = - \frac{40000 x}{( 3 + x ^{2} + 2 y ^{2} ) ^{2}}

y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}; f \neq = 0

Solution steps

f = - \frac{40000 x}{( 3 + x ^{2} + 2 y ^{2} ) ^{2}}

Multiply both sides by

(3 + x^{2} + 2 y^{2})^{2}

f (3 + x^{2} + 2 y^{2})^{2} = - 40000 x

Solve

f (3 + x^{2} + 2 y^{2})^{2} = - 40000 x : y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}; f \neq = 0

y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}; f \neq = 0

f (x) = (x^{3} - 3 x) (y + 3) + y (y + 6)

4 h^{3} - 96 h^{2} + 527 h

f (x) = 25 x^{2} - 25 y^{2} + 200 x + 200 y + 200

x^{2} + y^{2} + 6 x - 10 y + 5

y = - 5 x^{3} + 4 x^{2} + 5 x - 1

What is the answer to solvefor y,f=-(40000x)/((3+x^2+2y^2)^2) ?
The answer to solvefor y,f=-(40000x)/((3+x^2+2y^2)^2) is