2x/x^2-4div1/x+2 eching

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

Baholash

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

Qisqa yechim qadamlari

\frac{2x}{x^{2}-4} ni \frac{1}{x+2} ga bo'lish \frac{2x}{x^{2}-4} ga k'paytirish \frac{1}{x+2} ga qaytarish.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x+2 ni qisqartiring.

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

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

\frac{2x}{x^{2}-4} ni \frac{1}{x+2} ga bo'lish \frac{2x}{x^{2}-4} ga k'paytirish \frac{1}{x+2} ga qaytarish.

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

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

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

Surat va maxrajdagi ikkala x+2 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x}{x-2})$$

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

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

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

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

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}-2\right)\times 2x^{0}-2x^{1}x^{0}}{\left(x^{1}-2\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\times 2x^{0}-2\times 2x^{0}-2x^{1}x^{0}}{\left(x^{1}-2\right)^{2}}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$\frac{2x^{1}-2\times 2x^{0}-2x^{1}}{\left(x^{1}-2\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{2x^{1}-4x^{0}-2x^{1}}{\left(x^{1}-2\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(2-2\right)x^{1}-4x^{0}}{\left(x^{1}-2\right)^{2}}$$

2 dan 2 ni ayirish.

$$\frac{-4x^{0}}{\left(x^{1}-2\right)^{2}}$$

Har qanday t sharti uchun t^{1}=t.

$$\frac{-4x^{0}}{\left(x-2\right)^{2}}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

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