x^2+x+1/x^2-1*x^2-2x+1/x^3-1 eching

$$\frac { x ^ { 2 } + x + 1 } { x ^ { 2 } - 1 } \cdot \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 3 } - 1 }$$

Baholash

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

Qisqa yechim qadamlari

\frac{x^{2}-2x+1}{x^{3}-1} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-1 ni qisqartiring.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x^{2}+x+1}{x^{2}-1} ni \frac{x-1}{x^{2}+x+1} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala x^{2}+x+1 ni qisqartiring.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-1 ni qisqartiring.

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

Kengaytirish

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

Qisqa yechim qadamlari

\frac{x^{2}-2x+1}{x^{3}-1} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-1 ni qisqartiring.

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{x^{2}+x+1}{x^{2}-1} ni \frac{x-1}{x^{2}+x+1} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala x^{2}+x+1 ni qisqartiring.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-1 ni qisqartiring.

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