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

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

Baholash

$$\frac{3xy}{2\left(x^{2}-y^{2}\right)}$$

Qisqa yechim qadamlari

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

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

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

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

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

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

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

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

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

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

Faktor: 2x-2y.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x+y\right)\left(x-y\right) va 2\left(x-y\right) ning eng kichik umumiy karralisi 2\left(x+y\right)\left(x-y\right). \frac{xy}{\left(x+y\right)\left(x-y\right)} ni \frac{2}{2} marotabaga ko'paytirish. \frac{y}{2\left(x-y\right)} ni \frac{x+y}{x+y} marotabaga ko'paytirish.

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

\frac{2xy}{2\left(x+y\right)\left(x-y\right)} va \frac{y\left(x+y\right)}{2\left(x+y\right)\left(x-y\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

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

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

$$\frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2x^{2}-2y^{2}}$$

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

$$\frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)}-\frac{y^{2}}{2\left(x+y\right)\left(x-y\right)}$$

\frac{y^{2}+3xy}{2\left(x+y\right)\left(x-y\right)} va \frac{y^{2}}{2\left(x+y\right)\left(x-y\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{y^{2}+3xy-y^{2}}{2\left(x+y\right)\left(x-y\right)}$$

y^{2}+3xy-y^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{3xy}{2\left(x+y\right)\left(x-y\right)}$$

2\left(x+y\right)\left(x-y\right) ni kengaytirish.

$$\frac{3xy}{2x^{2}-2y^{2}}$$

Omil

$$\frac{3xy}{2\left(x^{2}-y^{2}\right)}$$