xy/x-y*(x/y-y/x) eching

$$\frac { x y } { x - y } \cdot ( \frac { x } { y } - \frac { y } { x } )$$

Baholash

$$x+y$$

Qisqa yechim qadamlari

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

$$\frac{xy}{x-y}\left(\frac{xx}{xy}-\frac{yy}{xy}\right)$$

\frac{xx}{xy} va \frac{yy}{xy} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{xy}{x-y}\times \frac{xx-yy}{xy}$$

xx-yy ichidagi ko‘paytirishlarni bajaring.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{xy}{x-y} ni \frac{x^{2}-y^{2}}{xy} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala xy ni qisqartiring.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-y ni qisqartiring.

$$x+y$$

Kengaytirish

$$x+y$$

Qisqa yechim qadamlari

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

$$\frac{xy}{x-y}\left(\frac{xx}{xy}-\frac{yy}{xy}\right)$$

\frac{xx}{xy} va \frac{yy}{xy} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{xy}{x-y}\times \frac{xx-yy}{xy}$$

xx-yy ichidagi ko‘paytirishlarni bajaring.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{xy}{x-y} ni \frac{x^{2}-y^{2}}{xy} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala xy ni qisqartiring.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-y ni qisqartiring.

$$x+y$$