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

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

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

simplify

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

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

Solution steps

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

Multiply by the conjugate

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

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

Cancel the common factor:

y^{2}

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

\frac{6600 x [ ( 1.04 ) ^{12} - 1 ]}{( 0.04 )}

s^{27} d^{62} \frac{z}{a}

(y + 1)^{5}

16.1 (\frac{15}{cos ( a )})^{2}

(\frac{27 a ^{12}}{t ^{15}})^{\frac{- 2}{3}}

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