What is ((y^2))/((sqrt(x^2+y^2)+x)) ?

The solution to ((y^2))/((sqrt(x^2+y^2)+x)) is sqrt(y^2+x^2)-x

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simplify ((y^2))/((sqrt(x^2+y^2)+x))

simplify

\frac{( y ^{2} )}{( x ^{2} + y ^{2} + x )}

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

Solution steps

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

Multiply by the conjugate

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

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

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

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

Cancel the common factor:

y^{2}

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

(4 a + 3 b)^{3}

10 a^{4} - b^{4}

6 x^{3} - 9 x^{2} y - 6 x^{2} y^{2}

\frac{x}{( x - 1 )} - \frac{1}{( x ^{2} - x )}

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

What is ((y^2))/((sqrt(x^2+y^2)+x)) ?
The solution to ((y^2))/((sqrt(x^2+y^2)+x)) is sqrt(y^2+x^2)-x