x/x-1+2/x+1-x^2+1/x^2-1 eching

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

Baholash

$$\frac{3}{x+1}$$

Qisqa yechim qadamlari

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

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

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

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

x\left(x+1\right)+2\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

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

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

$$\frac{x^{2}+3x-2}{\left(x-1\right)\left(x+1\right)}-\frac{x^{2}+1}{x^{2}-1}$$

Faktor: x^{2}-1.

$$\frac{x^{2}+3x-2}{\left(x-1\right)\left(x+1\right)}-\frac{x^{2}+1}{\left(x-1\right)\left(x+1\right)}$$

\frac{x^{2}+3x-2}{\left(x-1\right)\left(x+1\right)} va \frac{x^{2}+1}{\left(x-1\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x^{2}+3x-2-\left(x^{2}+1\right)}{\left(x-1\right)\left(x+1\right)}$$

x^{2}+3x-2-\left(x^{2}+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}+3x-2-x^{2}-1}{\left(x-1\right)\left(x+1\right)}$$

x^{2}+3x-2-x^{2}-1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{3x-3}{\left(x-1\right)\left(x+1\right)}$$

\frac{3x-3}{\left(x-1\right)\left(x+1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}$$

Surat va maxrajdagi ikkala x-1 ni qisqartiring.

$$\frac{3}{x+1}$$

Kengaytirish

$$\frac{3}{x+1}$$

Qisqa yechim qadamlari

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

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

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

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

x\left(x+1\right)+2\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

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

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

$$\frac{x^{2}+3x-2}{\left(x-1\right)\left(x+1\right)}-\frac{x^{2}+1}{x^{2}-1}$$

Faktor: x^{2}-1.

$$\frac{x^{2}+3x-2}{\left(x-1\right)\left(x+1\right)}-\frac{x^{2}+1}{\left(x-1\right)\left(x+1\right)}$$

\frac{x^{2}+3x-2}{\left(x-1\right)\left(x+1\right)} va \frac{x^{2}+1}{\left(x-1\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x^{2}+3x-2-\left(x^{2}+1\right)}{\left(x-1\right)\left(x+1\right)}$$

x^{2}+3x-2-\left(x^{2}+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}+3x-2-x^{2}-1}{\left(x-1\right)\left(x+1\right)}$$

x^{2}+3x-2-x^{2}-1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{3x-3}{\left(x-1\right)\left(x+1\right)}$$

\frac{3x-3}{\left(x-1\right)\left(x+1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{3\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}$$

Surat va maxrajdagi ikkala x-1 ni qisqartiring.

$$\frac{3}{x+1}$$