3/x-6-2/x+2 eching

$$\frac { 3 } { x - 6 } - \frac { 2 } { x + 2 }$$

Baholash

$$\frac{x+18}{\left(x-6\right)\left(x+2\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-6 va x+2 ning eng kichik umumiy karralisi \left(x-6\right)\left(x+2\right). \frac{3}{x-6} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{2}{x+2} ni \frac{x-6}{x-6} marotabaga ko'paytirish.

$$\frac{3\left(x+2\right)}{\left(x-6\right)\left(x+2\right)}-\frac{2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)}$$

\frac{3\left(x+2\right)}{\left(x-6\right)\left(x+2\right)} va \frac{2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{3\left(x+2\right)-2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)}$$

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

$$\frac{3x+6-2x+12}{\left(x-6\right)\left(x+2\right)}$$

3x+6-2x+12 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x+18}{\left(x-6\right)\left(x+2\right)}$$

\left(x-6\right)\left(x+2\right) ni kengaytirish.

$$\frac{x+18}{x^{2}-4x-12}$$

x ga nisbatan hosilani topish

$$\frac{60-36x-x^{2}}{x^{4}-8x^{3}-8x^{2}+96x+144}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-6 va x+2 ning eng kichik umumiy karralisi \left(x-6\right)\left(x+2\right). \frac{3}{x-6} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{2}{x+2} ni \frac{x-6}{x-6} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+2\right)}{\left(x-6\right)\left(x+2\right)}-\frac{2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)})$$

\frac{3\left(x+2\right)}{\left(x-6\right)\left(x+2\right)} va \frac{2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x+2\right)-2\left(x-6\right)}{\left(x-6\right)\left(x+2\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+6-2x+12}{\left(x-6\right)\left(x+2\right)})$$

3x+6-2x+12 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+18}{\left(x-6\right)\left(x+2\right)})$$

x-6 ifodaning har bir elementini x+2 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+18}{x^{2}+2x-6x-12})$$

-4x ni olish uchun 2x va -6x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+18}{x^{2}-4x-12})$$

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

$$\frac{\left(x^{2}-4x^{1}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+18)-\left(x^{1}+18\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x^{1}-12)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

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

$$\frac{\left(x^{2}-4x^{1}-12\right)x^{1-1}-\left(x^{1}+18\right)\left(2x^{2-1}-4x^{1-1}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-4x^{1}-12\right)x^{0}-\left(x^{1}+18\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

x^{2}-4x^{1}-12 ni x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}x^{0}-4x^{1}x^{0}-12x^{0}-\left(x^{1}+18\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

x^{1}+18 ni 2x^{1}-4x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}x^{0}-4x^{1}x^{0}-12x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\left(-4\right)x^{0}+18\times 2x^{1}+18\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

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

$$\frac{x^{2}-4x^{1}-12x^{0}-\left(2x^{1+1}-4x^{1}+18\times 2x^{1}+18\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

Qisqartirish.

$$\frac{x^{2}-4x^{1}-12x^{0}-\left(2x^{2}-4x^{1}+36x^{1}-72x^{0}\right)}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-x^{2}-36x^{1}+60x^{0}}{\left(x^{2}-4x^{1}-12\right)^{2}}$$

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

$$\frac{-x^{2}-36x+60x^{0}}{\left(x^{2}-4x-12\right)^{2}}$$

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

$$\frac{-x^{2}-36x+60\times 1}{\left(x^{2}-4x-12\right)^{2}}$$

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

$$\frac{-x^{2}-36x+60}{\left(x^{2}-4x-12\right)^{2}}$$