Réitigh =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}

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

Luacháil

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

Céimeanna gearra réitigh

Roinn \frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}} faoi \frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y} trí \frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}} a mhéadú faoi dheilín \frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y}.

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

Mar shampla \left(\sqrt{x^{2}+y^{2}}-y\right)\left(\sqrt{x^{2}+y^{2}}+y\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ríomh cumhacht \sqrt{x^{2}+y^{2}} de 2 agus faigh x^{2}+y^{2}.

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

Comhcheangail y^{2} agus -y^{2} chun 0 a fháil.

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

Mar shampla \left(x-\sqrt{x^{2}-y^{2}}\right)\left(\sqrt{x^{2}-y^{2}}+x\right). Is féidir iolrúchán a athrú ó bhonn go dtí difríocht na gcearnóg ag úsáid na rialach seo: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Ríomh cumhacht \sqrt{x^{2}-y^{2}} de 2 agus faigh x^{2}-y^{2}.

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

Chun an mhalairt ar x^{2}-y^{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Comhcheangail x^{2} agus -x^{2} chun 0 a fháil.

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

Difreálaigh w.r.t. x

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