簡約 ((x^2*y^2))/((sqrt(x^2+y^2)-x))

解

簡約

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

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

解答ステップ

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

共役で乗じる

\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}}

共通因数を約分する:

y^{2}

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