x^2-5x+6/x^3-6x^2+12x-8*(4-x/x-3+2) eching

$$\frac { x ^ { 2 } - 5 x + 6 } { x ^ { 3 } - 6 x ^ { 2 } + 12 x - 8 } \cdot ( \frac { 4 - x } { x - 3 } + 2 )$$

Baholash

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

Qisqa yechim qadamlari

\frac{x^{2}-5x+6}{x^{3}-6x^{2}+12x-8} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-2 ni qisqartiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{x-3}{x-3} marotabaga ko'paytirish.

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

\frac{4-x}{x-3} va \frac{2\left(x-3\right)}{x-3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

4-x+2\left(x-3\right) ichidagi ko‘paytirishlarni bajaring.

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

4-x+2x-6 kabi iboralarga o‘xshab birlashtiring.

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

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

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

Surat va maxrajdagi ikkala \left(x-3\right)\left(x-2\right) ni qisqartiring.

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

Kengaytirish

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

Qisqa yechim qadamlari

\frac{x^{2}-5x+6}{x^{3}-6x^{2}+12x-8} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-2 ni qisqartiring.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 ni \frac{x-3}{x-3} marotabaga ko'paytirish.

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

\frac{4-x}{x-3} va \frac{2\left(x-3\right)}{x-3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

4-x+2\left(x-3\right) ichidagi ko‘paytirishlarni bajaring.

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

4-x+2x-6 kabi iboralarga o‘xshab birlashtiring.

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

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

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

Surat va maxrajdagi ikkala \left(x-3\right)\left(x-2\right) ni qisqartiring.

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