x-1/x^2+4x+3+2/x^2+5x+6 eching

$$\frac { x - 1 } { x ^ { 2 } + 4 x + 3 } + \frac { 2 } { x ^ { 2 } + 5 x + 6 }$$

Baholash

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

Qisqa yechim qadamlari

Faktor: x^{2}+4x+3. Faktor: x^{2}+5x+6.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x+1\right)\left(x+3\right) va \left(x+2\right)\left(x+3\right) ning eng kichik umumiy karralisi \left(x+1\right)\left(x+2\right)\left(x+3\right). \frac{x-1}{\left(x+1\right)\left(x+3\right)} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{2}{\left(x+2\right)\left(x+3\right)} ni \frac{x+1}{x+1} marotabaga ko'paytirish.

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

\frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} va \frac{2\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

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

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

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

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

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

Surat va maxrajdagi ikkala x+3 ni qisqartiring.

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

\left(x+1\right)\left(x+2\right) ni kengaytirish.

$$\frac{x}{x^{2}+3x+2}$$

Kengaytirish

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

Qisqa yechim qadamlari

Faktor: x^{2}+4x+3. Faktor: x^{2}+5x+6.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x+1\right)\left(x+3\right) va \left(x+2\right)\left(x+3\right) ning eng kichik umumiy karralisi \left(x+1\right)\left(x+2\right)\left(x+3\right). \frac{x-1}{\left(x+1\right)\left(x+3\right)} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{2}{\left(x+2\right)\left(x+3\right)} ni \frac{x+1}{x+1} marotabaga ko'paytirish.

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

\frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} va \frac{2\left(x+1\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

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

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

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

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

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

Surat va maxrajdagi ikkala x+3 ni qisqartiring.

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

\left(x+1\right)\left(x+2\right) ni kengaytirish.

$$\frac{x}{x^{2}+3x+2}$$