1/x+1divx/x-2= eching

$$\frac{ 1 }{ x+1 } \div \frac{ x }{ x-2 } =$$

Baholash

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

Qisqa yechim qadamlari

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

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

x+1 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

x+1 ga x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

Qisqartirish.

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

x^{2}+x^{1} ni x^{0} marotabaga ko'paytirish.

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

x^{1}-2 ni 2x^{1}+x^{0} marotabaga ko'paytirish.

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

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

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

Qisqartirish.

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

O'xshash hadlarni birlashtirish.

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

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

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

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

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

Har qanday t sharti uchun t\times 1=t va 1t=t.

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