x/x-3+x+1/x^2+9+2/x^2-6x+9 eching

$$\frac{ x }{ x-3 } + \frac{ x+1 }{ { x }^{ 2 } +9 } + \frac{ 2 }{ { x }^{ 2 } -6x+9 }$$

Baholash

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-3 va x^{2}+9 ning eng kichik umumiy karralisi \left(x-3\right)\left(x^{2}+9\right). \frac{x}{x-3} ni \frac{x^{2}+9}{x^{2}+9} marotabaga ko'paytirish. \frac{x+1}{x^{2}+9} ni \frac{x-3}{x-3} marotabaga ko'paytirish.

$$\frac{x\left(x^{2}+9\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

\frac{x\left(x^{2}+9\right)}{\left(x-3\right)\left(x^{2}+9\right)} va \frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{x\left(x^{2}+9\right)+\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

x\left(x^{2}+9\right)+\left(x+1\right)\left(x-3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{3}+9x+x^{2}-3x+x-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

x^{3}+9x+x^{2}-3x+x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Faktor: x^{2}-6x+9.

$$\frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{\left(x-3\right)^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-3\right)\left(x^{2}+9\right) va \left(x-3\right)^{2} ning eng kichik umumiy karralisi \left(x-3\right)^{2}\left(x^{2}+9\right). \frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)} ni \frac{x-3}{x-3} marotabaga ko'paytirish. \frac{2}{\left(x-3\right)^{2}} ni \frac{x^{2}+9}{x^{2}+9} marotabaga ko'paytirish.

$$\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}+\frac{2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)} va \frac{2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)+2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)+2\left(x^{2}+9\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{4}-3x^{3}+7x^{2}-21x+x^{3}-3x^{2}-3x+9+2x^{2}+18}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

x^{4}-3x^{3}+7x^{2}-21x+x^{3}-3x^{2}-3x+9+2x^{2}+18 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

\left(x-3\right)^{2}\left(x^{2}+9\right) ni kengaytirish.

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{x^{4}-6x^{3}+18x^{2}-54x+81}$$

Kengaytirish

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-3 va x^{2}+9 ning eng kichik umumiy karralisi \left(x-3\right)\left(x^{2}+9\right). \frac{x}{x-3} ni \frac{x^{2}+9}{x^{2}+9} marotabaga ko'paytirish. \frac{x+1}{x^{2}+9} ni \frac{x-3}{x-3} marotabaga ko'paytirish.

$$\frac{x\left(x^{2}+9\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

\frac{x\left(x^{2}+9\right)}{\left(x-3\right)\left(x^{2}+9\right)} va \frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{x\left(x^{2}+9\right)+\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

x\left(x^{2}+9\right)+\left(x+1\right)\left(x-3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{3}+9x+x^{2}-3x+x-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

x^{3}+9x+x^{2}-3x+x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{x^{2}-6x+9}$$

Faktor: x^{2}-6x+9.

$$\frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)}+\frac{2}{\left(x-3\right)^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-3\right)\left(x^{2}+9\right) va \left(x-3\right)^{2} ning eng kichik umumiy karralisi \left(x-3\right)^{2}\left(x^{2}+9\right). \frac{x^{3}+7x+x^{2}-3}{\left(x-3\right)\left(x^{2}+9\right)} ni \frac{x-3}{x-3} marotabaga ko'paytirish. \frac{2}{\left(x-3\right)^{2}} ni \frac{x^{2}+9}{x^{2}+9} marotabaga ko'paytirish.

$$\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}+\frac{2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)} va \frac{2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)+2\left(x^{2}+9\right)}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

\left(x^{3}+7x+x^{2}-3\right)\left(x-3\right)+2\left(x^{2}+9\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{4}-3x^{3}+7x^{2}-21x+x^{3}-3x^{2}-3x+9+2x^{2}+18}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

x^{4}-3x^{3}+7x^{2}-21x+x^{3}-3x^{2}-3x+9+2x^{2}+18 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{\left(x-3\right)^{2}\left(x^{2}+9\right)}$$

\left(x-3\right)^{2}\left(x^{2}+9\right) ni kengaytirish.

$$\frac{x^{4}-2x^{3}+6x^{2}-24x+27}{x^{4}-6x^{3}+18x^{2}-54x+81}$$