2/x+2-7/x-3 eching

$$\frac{ 2 }{ x+2 } - \frac{ 7 }{ x-3 }$$

Baholash

$$-\frac{5\left(x+4\right)}{\left(x-3\right)\left(x+2\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+2 va x-3 ning eng kichik umumiy karralisi \left(x-3\right)\left(x+2\right). \frac{2}{x+2} ni \frac{x-3}{x-3} marotabaga ko'paytirish. \frac{7}{x-3} ni \frac{x+2}{x+2} marotabaga ko'paytirish.

$$\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}-\frac{7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)}$$

\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)} va \frac{7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{2\left(x-3\right)-7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)}$$

2\left(x-3\right)-7\left(x+2\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2x-6-7x-14}{\left(x-3\right)\left(x+2\right)}$$

2x-6-7x-14 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-5x-20}{\left(x-3\right)\left(x+2\right)}$$

\left(x-3\right)\left(x+2\right) ni kengaytirish.

$$\frac{-5x-20}{x^{2}-x-6}$$

x ga nisbatan hosilani topish

$$\frac{5\left(\left(x+4\right)^{2}-14\right)}{\left(\left(x-3\right)\left(x+2\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+2 va x-3 ning eng kichik umumiy karralisi \left(x-3\right)\left(x+2\right). \frac{2}{x+2} ni \frac{x-3}{x-3} marotabaga ko'paytirish. \frac{7}{x-3} ni \frac{x+2}{x+2} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}-\frac{7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)})$$

\frac{2\left(x-3\right)}{\left(x-3\right)\left(x+2\right)} va \frac{7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x-3\right)-7\left(x+2\right)}{\left(x-3\right)\left(x+2\right)})$$

2\left(x-3\right)-7\left(x+2\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-6-7x-14}{\left(x-3\right)\left(x+2\right)})$$

2x-6-7x-14 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x-20}{\left(x-3\right)\left(x+2\right)})$$

x-3 ifodaning har bir elementini x+2 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x-20}{x^{2}+2x-3x-6})$$

-x ni olish uchun 2x va -3x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x-20}{x^{2}-x-6})$$

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

$$\frac{\left(x^{2}-x^{1}-6\right)\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{1}-20)-\left(-5x^{1}-20\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-6)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

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

$$\frac{\left(x^{2}-x^{1}-6\right)\left(-5\right)x^{1-1}-\left(-5x^{1}-20\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-x^{1}-6\right)\left(-5\right)x^{0}-\left(-5x^{1}-20\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

x^{2}-x^{1}-6 ni -5x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\left(-5\right)x^{0}-x^{1}\left(-5\right)x^{0}-6\left(-5\right)x^{0}-\left(-5x^{1}-20\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

-5x^{1}-20 ni 2x^{1}-x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\left(-5\right)x^{0}-x^{1}\left(-5\right)x^{0}-6\left(-5\right)x^{0}-\left(-5x^{1}\times 2x^{1}-5x^{1}\left(-1\right)x^{0}-20\times 2x^{1}-20\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

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

$$\frac{-5x^{2}-\left(-5x^{1}\right)-6\left(-5\right)x^{0}-\left(-5\times 2x^{1+1}-5\left(-1\right)x^{1}-20\times 2x^{1}-20\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

Qisqartirish.

$$\frac{-5x^{2}+5x^{1}+30x^{0}-\left(-10x^{2}+5x^{1}-40x^{1}+20x^{0}\right)}{\left(x^{2}-x^{1}-6\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{5x^{2}+40x^{1}+10x^{0}}{\left(x^{2}-x^{1}-6\right)^{2}}$$

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

$$\frac{5x^{2}+40x+10x^{0}}{\left(x^{2}-x-6\right)^{2}}$$

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

$$\frac{5x^{2}+40x+10\times 1}{\left(x^{2}-x-6\right)^{2}}$$

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

$$\frac{5x^{2}+40x+10}{\left(x^{2}-x-6\right)^{2}}$$