f(x)=(x^2+4x+3/x^2+2x-3-x^2+2x+1/x^2+3x+2)*x+2/x+1 eching

$$f ( x ) = ( \frac { x ^ { 2 } + 4 x + 3 } { x ^ { 2 } + 2 x - 3 } - \frac { x ^ { 2 } + 2 x + 1 } { x ^ { 2 } + 3 x + 2 } ) \cdot \frac { x + 2 } { x + 1 }$$

Baholash

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

Qisqa yechim qadamlari

\frac{x^{2}+4x+3}{x^{2}+2x-3} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x+3 ni qisqartiring.

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

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

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

Surat va maxrajdagi ikkala x+1 ni qisqartiring.

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

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

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

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

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

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

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

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

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3x+3}{\left(x-1\right)\left(x+2\right)} ni \frac{x+2}{x+1} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala x+2 ni qisqartiring.

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

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

\frac{x^{2}+4x+3}{x^{2}+2x-3} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x+3 ni qisqartiring.

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

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

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

Surat va maxrajdagi ikkala x+1 ni qisqartiring.

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

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

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

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

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

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

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

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

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

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{3x+3}{\left(x-1\right)\left(x+2\right)} ni \frac{x+2}{x+1} ga ko‘paytiring.

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

Surat va maxrajdagi ikkala x+2 ni qisqartiring.

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

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.

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