Whakaoti i te =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}

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

Aromātai

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

Ngā Hipanga Rongoā Poto

Whakawehe \frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}} ki te \frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y} mā te whakarea \frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}} ki te tau huripoki o \frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y}.

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

Whakaarohia te \left(\sqrt{x^{2}+y^{2}}-y\right)\left(\sqrt{x^{2}+y^{2}}+y\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Tātaihia te \sqrt{x^{2}+y^{2}} mā te pū o 2, kia riro ko x^{2}+y^{2}.

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

Pahekotia te y^{2} me -y^{2}, ka 0.

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

Whakaarohia te \left(x-\sqrt{x^{2}-y^{2}}\right)\left(\sqrt{x^{2}-y^{2}}+x\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Tātaihia te \sqrt{x^{2}-y^{2}} mā te pū o 2, kia riro ko x^{2}-y^{2}.

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

Hei kimi i te tauaro o x^{2}-y^{2}, kimihia te tauaro o ia taurangi.

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

Pahekotia te x^{2} me -x^{2}, ka 0.

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

Kimi Pārōnaki e ai ki x

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