1/x^2-5x+6+1/x^2-3x+2+2/x^2-8x+15 eching

$$\frac { 1 } { x ^ { 2 } - 5 x + 6 } + \frac { 1 } { x ^ { 2 } - 3 x + 2 } + \frac { 2 } { x ^ { 2 } - 8 x + 15 }$$

Baholash

$$\frac{4}{\left(x-5\right)\left(x-1\right)}$$

Qisqa yechim qadamlari

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

$$\frac{1}{\left(x-3\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

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

$$\frac{x-1}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

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

$$\frac{x-1+x-3}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

x-1+x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

\frac{2x-4}{\left(x-3\right)\left(x-2\right)\left(x-1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{2\left(x-2\right)}{\left(x-3\right)\left(x-2\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Surat va maxrajdagi ikkala x-2 ni qisqartiring.

$$\frac{2}{\left(x-3\right)\left(x-1\right)}+\frac{2}{x^{2}-8x+15}$$

Faktor: x^{2}-8x+15.

$$\frac{2}{\left(x-3\right)\left(x-1\right)}+\frac{2}{\left(x-5\right)\left(x-3\right)}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-3\right)\left(x-1\right) va \left(x-5\right)\left(x-3\right) ning eng kichik umumiy karralisi \left(x-5\right)\left(x-3\right)\left(x-1\right). \frac{2}{\left(x-3\right)\left(x-1\right)} ni \frac{x-5}{x-5} marotabaga ko'paytirish. \frac{2}{\left(x-5\right)\left(x-3\right)} ni \frac{x-1}{x-1} marotabaga ko'paytirish.

$$\frac{2\left(x-5\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}+\frac{2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

\frac{2\left(x-5\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)} va \frac{2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2\left(x-5\right)+2\left(x-1\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

2\left(x-5\right)+2\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2x-10+2x-2}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

2x-10+2x-2 kabi iboralarga o‘xshab birlashtiring.

$$\frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

\frac{4x-12}{\left(x-5\right)\left(x-3\right)\left(x-1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{4\left(x-3\right)}{\left(x-5\right)\left(x-3\right)\left(x-1\right)}$$

Surat va maxrajdagi ikkala x-3 ni qisqartiring.

$$\frac{4}{\left(x-5\right)\left(x-1\right)}$$

\left(x-5\right)\left(x-1\right) ni kengaytirish.

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

x ga nisbatan hosilani topish

$$\frac{8\left(3-x\right)}{\left(\left(x-5\right)\left(x-1\right)\right)^{2}}$$