12/x^2+2x-2/x+6/x+2 eching

$$\frac{ 12 }{ { x }^{ 2 } +2x } - \frac{ 2 }{ x } + \frac{ 6 }{ x+2 }$$

Baholash

$$\frac{4}{x}$$

Qisqa yechim qadamlari

Faktor: x^{2}+2x.

$$\frac{12}{x\left(x+2\right)}-\frac{2}{x}+\frac{6}{x+2}$$

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

$$\frac{12}{x\left(x+2\right)}-\frac{2\left(x+2\right)}{x\left(x+2\right)}+\frac{6}{x+2}$$

\frac{12}{x\left(x+2\right)} va \frac{2\left(x+2\right)}{x\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{12-2\left(x+2\right)}{x\left(x+2\right)}+\frac{6}{x+2}$$

12-2\left(x+2\right) ichidagi ko‘paytirishlarni bajaring.

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

12-2x-4 kabi iboralarga o‘xshab birlashtiring.

$$\frac{8-2x}{x\left(x+2\right)}+\frac{6}{x+2}$$

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

$$\frac{8-2x}{x\left(x+2\right)}+\frac{6x}{x\left(x+2\right)}$$

\frac{8-2x}{x\left(x+2\right)} va \frac{6x}{x\left(x+2\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{8-2x+6x}{x\left(x+2\right)}$$

8-2x+6x kabi iboralarga o‘xshab birlashtiring.

$$\frac{8+4x}{x\left(x+2\right)}$$

\frac{8+4x}{x\left(x+2\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x+2 ni qisqartiring.

$$\frac{4}{x}$$

x ga nisbatan hosilani topish

$$-\frac{4}{x^{2}}$$

Derivativ ifodasidan foydalanish qadamlari

Faktor: x^{2}+2x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{x\left(x+2\right)}-\frac{2}{x}+\frac{6}{x+2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{x\left(x+2\right)}-\frac{2\left(x+2\right)}{x\left(x+2\right)}+\frac{6}{x+2})$$

\frac{12}{x\left(x+2\right)} va \frac{2\left(x+2\right)}{x\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12-2\left(x+2\right)}{x\left(x+2\right)}+\frac{6}{x+2})$$

12-2\left(x+2\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12-2x-4}{x\left(x+2\right)}+\frac{6}{x+2})$$

12-2x-4 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8-2x}{x\left(x+2\right)}+\frac{6}{x+2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8-2x}{x\left(x+2\right)}+\frac{6x}{x\left(x+2\right)})$$

\frac{8-2x}{x\left(x+2\right)} va \frac{6x}{x\left(x+2\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8-2x+6x}{x\left(x+2\right)})$$

8-2x+6x kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8+4x}{x\left(x+2\right)})$$

\frac{8+4x}{x\left(x+2\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+2\right)}{x\left(x+2\right)})$$

Surat va maxrajdagi ikkala x+2 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{x})$$

ax^{n} hosilasi – nax^{n-1}.

$$-4x^{-1-1}$$

-1 dan 1 ni ayirish.

$$-4x^{-2}$$