x-1/x^2+3x+2+6/2+x-x^2-10-x/4-x^2 eching

$$\frac { x - 1 } { x ^ { 2 } + 3 x + 2 } + \frac { 6 } { 2 + x - x ^ { 2 } } - \frac { 10 - x } { 4 - x ^ { 2 } }$$

Baholash

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Qisqa yechim qadamlari

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

$$\frac{x-1}{\left(x+1\right)\left(x+2\right)}+\frac{6}{\left(x-2\right)\left(-x-1\right)}-\frac{10-x}{4-x^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x+1\right)\left(x+2\right) va \left(x-2\right)\left(-x-1\right) ning eng kichik umumiy karralisi \left(x-2\right)\left(x+1\right)\left(x+2\right). \frac{x-1}{\left(x+1\right)\left(x+2\right)} ni \frac{x-2}{x-2} marotabaga ko'paytirish. \frac{6}{\left(x-2\right)\left(-x-1\right)} ni \frac{-\left(x+2\right)}{-\left(x+2\right)} marotabaga ko'paytirish.

$$\frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}+\frac{6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

\frac{\left(x-1\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} va \frac{6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(x-1\right)\left(x-2\right)+6\left(-1\right)\left(x+2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

\left(x-1\right)\left(x-2\right)+6\left(-1\right)\left(x+2\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}-2x-x+2-6x-12}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

x^{2}-2x-x+2-6x-12 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{2}-9x-10}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

\frac{x^{2}-9x-10}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\left(x-10\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Surat va maxrajdagi ikkala x+1 ni qisqartiring.

$$\frac{x-10}{\left(x-2\right)\left(x+2\right)}-\frac{10-x}{4-x^{2}}$$

Faktor: 4-x^{2}.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-2\right)\left(x+2\right) va \left(x-2\right)\left(-x-2\right) ning eng kichik umumiy karralisi \left(x-2\right)\left(x+2\right). \frac{10-x}{\left(x-2\right)\left(-x-2\right)} ni \frac{-1}{-1} marotabaga ko'paytirish.

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

\frac{x-10}{\left(x-2\right)\left(x+2\right)} va \frac{-\left(10-x\right)}{\left(x-2\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x-10-\left(-\left(10-x\right)\right) ichidagi ko‘paytirishlarni bajaring.

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

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

$$\frac{0}{\left(x-2\right)\left(x+2\right)}$$

Nolni nolga teng bo‘lmagan har qanday songa boʻlsangiz, natija nol chiqadi.

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Omil

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