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

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

Baholash

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

Qisqa yechim qadamlari

Faktor: x^{2}-4x+3.

$$\frac{-6}{\left(x-3\right)\left(x-1\right)}-\frac{3}{3-x}-\frac{4}{x-1}$$

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

$$\frac{-6}{\left(x-3\right)\left(x-1\right)}-\frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

\frac{-6}{\left(x-3\right)\left(x-1\right)} va \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{-6-3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

-6-3\left(-1\right)\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{-6+3x-3}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

-6+3x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-9+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

\frac{-9+3x}{\left(x-3\right)\left(x-1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-3 ni qisqartiring.

$$\frac{3}{x-1}-\frac{4}{x-1}$$

\frac{3}{x-1} va \frac{4}{x-1} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring. -1 olish uchun 3 dan 4 ni ayirish.

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

x ga nisbatan hosilani topish

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