(1/1+x+2x/1-x^2)*(1/x-1) eching

$$( \frac { 1 } { 1 + x } + \frac { 2 x } { 1 - x ^ { 2 } } ) \cdot ( \frac { 1 } { x } - 1 )$$

Baholash

$$\frac{1}{x}$$

Qisqa yechim qadamlari

Faktor: 1-x^{2}.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1+x va \left(x-1\right)\left(-x-1\right) ning eng kichik umumiy karralisi \left(x-1\right)\left(x+1\right). \frac{1}{1+x} ni \frac{x-1}{x-1} marotabaga ko'paytirish. \frac{2x}{\left(x-1\right)\left(-x-1\right)} ni \frac{-1}{-1} marotabaga ko'paytirish.

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

\frac{x-1}{\left(x-1\right)\left(x+1\right)} va \frac{-2x}{\left(x-1\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

x-1-2x kabi iboralarga o‘xshab birlashtiring.

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

-x-1 mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala x+1 ni qisqartiring.

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

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

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

\frac{1}{x} va \frac{x}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{-1}{x-1} ni \frac{1-x}{x} ga ko‘paytiring.

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

1-x mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala x-1 ni qisqartiring.

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

1 hosil qilish uchun -1 va -1 ni ko'paytirish.

$$\frac{1}{x}$$

Kengaytirish

$$\frac{1}{x}$$

Qisqa yechim qadamlari

Faktor: 1-x^{2}.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 1+x va \left(x-1\right)\left(-x-1\right) ning eng kichik umumiy karralisi \left(x-1\right)\left(x+1\right). \frac{1}{1+x} ni \frac{x-1}{x-1} marotabaga ko'paytirish. \frac{2x}{\left(x-1\right)\left(-x-1\right)} ni \frac{-1}{-1} marotabaga ko'paytirish.

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

\frac{x-1}{\left(x-1\right)\left(x+1\right)} va \frac{-2x}{\left(x-1\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

x-1-2x kabi iboralarga o‘xshab birlashtiring.

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

-x-1 mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala x+1 ni qisqartiring.

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

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

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

\frac{1}{x} va \frac{x}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{-1}{x-1} ni \frac{1-x}{x} ga ko‘paytiring.

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

1-x mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala x-1 ni qisqartiring.

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

1 hosil qilish uchun -1 va -1 ni ko'paytirish.

$$\frac{1}{x}$$