1/x-2-3/x+1 eching

$$\frac { 1 } { x - 2 } - \frac { 3 } { x + 1 }$$

Baholash

$$\frac{7-2x}{\left(x-2\right)\left(x+1\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-2 va x+1 ning eng kichik umumiy karralisi \left(x-2\right)\left(x+1\right). \frac{1}{x-2} ni \frac{x+1}{x+1} marotabaga ko'paytirish. \frac{3}{x+1} ni \frac{x-2}{x-2} marotabaga ko'paytirish.

$$\frac{x+1}{\left(x-2\right)\left(x+1\right)}-\frac{3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}$$

\frac{x+1}{\left(x-2\right)\left(x+1\right)} va \frac{3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x+1-3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}$$

x+1-3\left(x-2\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x+1-3x+6}{\left(x-2\right)\left(x+1\right)}$$

x+1-3x+6 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-2x+7}{\left(x-2\right)\left(x+1\right)}$$

\left(x-2\right)\left(x+1\right) ni kengaytirish.

$$\frac{-2x+7}{x^{2}-x-2}$$

x ga nisbatan hosilani topish

$$\frac{2x^{2}-14x+11}{x^{4}-2x^{3}-3x^{2}+4x+4}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-2 va x+1 ning eng kichik umumiy karralisi \left(x-2\right)\left(x+1\right). \frac{1}{x-2} ni \frac{x+1}{x+1} marotabaga ko'paytirish. \frac{3}{x+1} ni \frac{x-2}{x-2} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+1}{\left(x-2\right)\left(x+1\right)}-\frac{3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)})$$

\frac{x+1}{\left(x-2\right)\left(x+1\right)} va \frac{3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+1-3\left(x-2\right)}{\left(x-2\right)\left(x+1\right)})$$

x+1-3\left(x-2\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+1-3x+6}{\left(x-2\right)\left(x+1\right)})$$

x+1-3x+6 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2x+7}{\left(x-2\right)\left(x+1\right)})$$

x-2 ifodaning har bir elementini x+1 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2x+7}{x^{2}+x-2x-2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-2x+7}{x^{2}-x-2})$$

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

$$\frac{\left(x^{2}-x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{1}+7)-\left(-2x^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-2)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{\left(x^{2}-x^{1}-2\right)\left(-2\right)x^{1-1}-\left(-2x^{1}+7\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-x^{1}-2\right)\left(-2\right)x^{0}-\left(-2x^{1}+7\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{x^{2}\left(-2\right)x^{0}-x^{1}\left(-2\right)x^{0}-2\left(-2\right)x^{0}-\left(-2x^{1}+7\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

-2x^{1}+7 ni 2x^{1}-x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\left(-2\right)x^{0}-x^{1}\left(-2\right)x^{0}-2\left(-2\right)x^{0}-\left(-2x^{1}\times 2x^{1}-2x^{1}\left(-1\right)x^{0}+7\times 2x^{1}+7\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{-2x^{2}-\left(-2x^{1}\right)-2\left(-2\right)x^{0}-\left(-2\times 2x^{1+1}-2\left(-1\right)x^{1}+7\times 2x^{1}+7\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Qisqartirish.

$$\frac{-2x^{2}+2x^{1}+4x^{0}-\left(-4x^{2}+2x^{1}+14x^{1}-7x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{2x^{2}-14x^{1}+11x^{0}}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{2x^{2}-14x+11x^{0}}{\left(x^{2}-x-2\right)^{2}}$$

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

$$\frac{2x^{2}-14x+11\times 1}{\left(x^{2}-x-2\right)^{2}}$$

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

$$\frac{2x^{2}-14x+11}{\left(x^{2}-x-2\right)^{2}}$$