=frac{sqrt{x^{2}+y^{2}}-y}{x-sqrt{x^{2}-y^{2}}}divfrac{sqrt{x^2-y^2}+x}{sqrt{x^2+y^2}+y} eching

$$= \frac { \sqrt { x ^ { 2 } + y ^ { 2 } } - y } { x - \sqrt { x ^ { 2 } - y ^ { 2 } } } \div \frac { \sqrt { x ^ { 2 } - y ^ { 2 } } + x } { \sqrt { x ^ { 2 } + y ^ { 2 } } + y }$$

Baholash

$$\left(\frac{x}{y}\right)^{2}$$

Qisqa yechim qadamlari

\frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}} ni \frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y} ga bo'lish \frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}} ga k'paytirish \frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y} ga qaytarish.

$$\frac{\left(\sqrt{x^{2}+y^{2}}-y\right)\left(\sqrt{x^{2}+y^{2}}+y\right)}{\left(x-\sqrt{x^{2}-y^{2}}\right)\left(\sqrt{x^{2}-y^{2}}+x\right)}$$

Hisoblang: \left(\sqrt{x^{2}+y^{2}}-y\right)\left(\sqrt{x^{2}+y^{2}}+y\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\left(\sqrt{x^{2}+y^{2}}\right)^{2}-y^{2}}{\left(x-\sqrt{x^{2}-y^{2}}\right)\left(\sqrt{x^{2}-y^{2}}+x\right)}$$

2 daraja ko‘rsatkichini \sqrt{x^{2}+y^{2}} ga hisoblang va x^{2}+y^{2} ni qiymatni oling.

$$\frac{x^{2}+y^{2}-y^{2}}{\left(x-\sqrt{x^{2}-y^{2}}\right)\left(\sqrt{x^{2}-y^{2}}+x\right)}$$

0 ni olish uchun y^{2} va -y^{2} ni birlashtirish.

$$\frac{x^{2}}{\left(x-\sqrt{x^{2}-y^{2}}\right)\left(\sqrt{x^{2}-y^{2}}+x\right)}$$

Hisoblang: \left(x-\sqrt{x^{2}-y^{2}}\right)\left(\sqrt{x^{2}-y^{2}}+x\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{x^{2}}{x^{2}-\left(\sqrt{x^{2}-y^{2}}\right)^{2}}$$

2 daraja ko‘rsatkichini \sqrt{x^{2}-y^{2}} ga hisoblang va x^{2}-y^{2} ni qiymatni oling.

$$\frac{x^{2}}{x^{2}-\left(x^{2}-y^{2}\right)}$$

x^{2}-y^{2} teskarisini topish uchun har birining teskarisini toping.

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

0 ni olish uchun x^{2} va -x^{2} ni birlashtirish.

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

x ga nisbatan hosilani topish

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