x-y/x+y-x+y/x-y/1-frac{x^2-xy-y^2{x^2-y^2}} eching

$$\frac { \frac { x - y } { x + y } - \frac { x + y } { x - y } } { 1 - \frac { x ^ { 2 } - x y - y ^ { 2 } } { x ^ { 2 } - y ^ { 2 } } }$$

Baholash

$$-4$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+y va x-y ning eng kichik umumiy karralisi \left(x+y\right)\left(x-y\right). \frac{x-y}{x+y} ni \frac{x-y}{x-y} marotabaga ko'paytirish. \frac{x+y}{x-y} ni \frac{x+y}{x+y} marotabaga ko'paytirish.

$$\frac{\frac{\left(x-y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}-\frac{\left(x+y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}}{1-\frac{x^{2}-xy-y^{2}}{x^{2}-y^{2}}}$$

\frac{\left(x-y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} va \frac{\left(x+y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{\left(x-y\right)\left(x-y\right)-\left(x+y\right)\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}}{1-\frac{x^{2}-xy-y^{2}}{x^{2}-y^{2}}}$$

\left(x-y\right)\left(x-y\right)-\left(x+y\right)\left(x+y\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{x^{2}-xy-xy+y^{2}-x^{2}-xy-xy-y^{2}}{\left(x+y\right)\left(x-y\right)}}{1-\frac{x^{2}-xy-y^{2}}{x^{2}-y^{2}}}$$

x^{2}-xy-xy+y^{2}-x^{2}-xy-xy-y^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{1-\frac{x^{2}-xy-y^{2}}{x^{2}-y^{2}}}$$

Faktor: x^{2}-y^{2}.

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{1-\frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} marotabaga ko'paytirish.

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)}-\frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)}}$$

\frac{\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)} va \frac{x^{2}-xy-y^{2}}{\left(x+y\right)\left(x-y\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{\left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right)}{\left(x+y\right)\left(x-y\right)}}$$

\left(x+y\right)\left(x-y\right)-\left(x^{2}-xy-y^{2}\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2}}{\left(x+y\right)\left(x-y\right)}}$$

x^{2}-xy+yx-y^{2}-x^{2}+xy+y^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{-4xy}{\left(x+y\right)\left(x-y\right)}}{\frac{xy}{\left(x+y\right)\left(x-y\right)}}$$

\frac{-4xy}{\left(x+y\right)\left(x-y\right)} ni \frac{xy}{\left(x+y\right)\left(x-y\right)} ga bo'lish \frac{-4xy}{\left(x+y\right)\left(x-y\right)} ga k'paytirish \frac{xy}{\left(x+y\right)\left(x-y\right)} ga qaytarish.

$$\frac{-4xy\left(x+y\right)\left(x-y\right)}{\left(x+y\right)\left(x-y\right)xy}$$

Surat va maxrajdagi ikkala xy\left(x+y\right)\left(x-y\right) ni qisqartiring.

$$-4$$

Omil

$$-4$$