x^-1+y^-1/x^-1y-y^-1x eching

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

Baholash

$$-\frac{1}{x-y}$$

Qisqa yechim qadamlari

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\left(1+\frac{1}{y}x\right)\times \frac{1}{x}}{\frac{1}{x}\times \frac{1}{y}\left(x-y\right)\left(-x-y\right)}$$

Surat va maxrajdagi ikkala \frac{1}{x} ni qisqartiring.

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

Ifodani kengaytiring.

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

\frac{1}{y}x ni yagona kasrga aylantiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{y}{y} marotabaga ko'paytirish.

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

\frac{y}{y} va \frac{x}{y} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\frac{1}{y}x^{2} ni yagona kasrga aylantiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. y ni \frac{y}{y} marotabaga ko'paytirish.

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

-\frac{x^{2}}{y} va \frac{yy}{y} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

-x^{2}+yy ichidagi ko‘paytirishlarni bajaring.

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

\frac{y+x}{y} ni \frac{-x^{2}+y^{2}}{y} ga bo'lish \frac{y+x}{y} ga k'paytirish \frac{-x^{2}+y^{2}}{y} ga qaytarish.

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

Surat va maxrajdagi ikkala y ni qisqartiring.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

y+x mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala -x-y ni qisqartiring.

$$\frac{-1}{x-y}$$

Kengaytirish

$$\frac{1}{y-x}$$

Qisqa yechim qadamlari

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\left(1+\frac{1}{y}x\right)\times \frac{1}{x}}{\frac{1}{x}\times \frac{1}{y}\left(x-y\right)\left(-x-y\right)}$$

Surat va maxrajdagi ikkala \frac{1}{x} ni qisqartiring.

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

Ifodani kengaytiring.

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

\frac{1}{y}x ni yagona kasrga aylantiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1 ni \frac{y}{y} marotabaga ko'paytirish.

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

\frac{y}{y} va \frac{x}{y} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\frac{1}{y}x^{2} ni yagona kasrga aylantiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. y ni \frac{y}{y} marotabaga ko'paytirish.

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

-\frac{x^{2}}{y} va \frac{yy}{y} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

-x^{2}+yy ichidagi ko‘paytirishlarni bajaring.

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

\frac{y+x}{y} ni \frac{-x^{2}+y^{2}}{y} ga bo'lish \frac{y+x}{y} ga k'paytirish \frac{-x^{2}+y^{2}}{y} ga qaytarish.

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

Surat va maxrajdagi ikkala y ni qisqartiring.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

y+x mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala -x-y ni qisqartiring.

$$\frac{-1}{x-y}$$