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

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

Baholash

$$\frac{5x-4}{\left(x-2\right)\left(x+1\right)}$$

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{2}{x-2} ni \frac{x+1}{x+1} marotabaga ko'paytirish. \frac{3}{x+1} ni \frac{x-2}{x-2} marotabaga ko'paytirish.

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

\frac{2\left(x+1\right)}{\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 qo‘shish orqali qo‘shing.

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

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

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

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

$$\frac{5x-4}{\left(x-2\right)\left(x+1\right)}$$

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

$$\frac{5x-4}{x^{2}-x-2}$$

x ga nisbatan hosilani topish

$$\frac{-5x^{2}+8x-14}{\left(\left(x-2\right)\left(x+1\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

\frac{2\left(x+1\right)}{\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 qo‘shish orqali qo‘shing.

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-4}{\left(x-2\right)\left(x+1\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-4}{x^{2}+x-2x-2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-4}{x^{2}-x-2})$$

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

$$\frac{\left(x^{2}-x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1}-4)-\left(5x^{1}-4\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-2)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{\left(x^{2}-x^{1}-2\right)\times 5x^{1-1}-\left(5x^{1}-4\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-x^{1}-2\right)\times 5x^{0}-\left(5x^{1}-4\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{x^{2}\times 5x^{0}-x^{1}\times 5x^{0}-2\times 5x^{0}-\left(5x^{1}-4\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

5x^{1}-4 ni 2x^{1}-x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 5x^{0}-x^{1}\times 5x^{0}-2\times 5x^{0}-\left(5x^{1}\times 2x^{1}+5x^{1}\left(-1\right)x^{0}-4\times 2x^{1}-4\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{5x^{2}-5x^{1}-2\times 5x^{0}-\left(5\times 2x^{1+1}+5\left(-1\right)x^{1}-4\times 2x^{1}-4\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

Qisqartirish.

$$\frac{5x^{2}-5x^{1}-10x^{0}-\left(10x^{2}-5x^{1}-8x^{1}+4x^{0}\right)}{\left(x^{2}-x^{1}-2\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-5x^{2}+8x^{1}-14x^{0}}{\left(x^{2}-x^{1}-2\right)^{2}}$$

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

$$\frac{-5x^{2}+8x-14x^{0}}{\left(x^{2}-x-2\right)^{2}}$$

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

$$\frac{-5x^{2}+8x-14}{\left(x^{2}-x-2\right)^{2}}$$