6/x-4+5/x+3 eching

$$\frac { 6 } { x - 4 } + \frac { 5 } { x + 3 }$$

Baholash

$$\frac{11x-2}{\left(x-4\right)\left(x+3\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-4 va x+3 ning eng kichik umumiy karralisi \left(x-4\right)\left(x+3\right). \frac{6}{x-4} ni \frac{x+3}{x+3} marotabaga ko'paytirish. \frac{5}{x+3} ni \frac{x-4}{x-4} marotabaga ko'paytirish.

$$\frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}+\frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)}$$

\frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)} va \frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{6\left(x+3\right)+5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)}$$

6\left(x+3\right)+5\left(x-4\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{6x+18+5x-20}{\left(x-4\right)\left(x+3\right)}$$

6x+18+5x-20 kabi iboralarga o‘xshab birlashtiring.

$$\frac{11x-2}{\left(x-4\right)\left(x+3\right)}$$

\left(x-4\right)\left(x+3\right) ni kengaytirish.

$$\frac{11x-2}{x^{2}-x-12}$$

x ga nisbatan hosilani topish

$$\frac{-11x^{2}+4x-134}{\left(\left(x-4\right)\left(x+3\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-4 va x+3 ning eng kichik umumiy karralisi \left(x-4\right)\left(x+3\right). \frac{6}{x-4} ni \frac{x+3}{x+3} marotabaga ko'paytirish. \frac{5}{x+3} ni \frac{x-4}{x-4} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)}+\frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)})$$

\frac{6\left(x+3\right)}{\left(x-4\right)\left(x+3\right)} va \frac{5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6\left(x+3\right)+5\left(x-4\right)}{\left(x-4\right)\left(x+3\right)})$$

6\left(x+3\right)+5\left(x-4\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x+18+5x-20}{\left(x-4\right)\left(x+3\right)})$$

6x+18+5x-20 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x-2}{\left(x-4\right)\left(x+3\right)})$$

x-4 ifodaning har bir elementini x+3 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x-2}{x^{2}+3x-4x-12})$$

-x ni olish uchun 3x va -4x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x-2}{x^{2}-x-12})$$

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

$$\frac{\left(x^{2}-x^{1}-12\right)\frac{\mathrm{d}}{\mathrm{d}x}(11x^{1}-2)-\left(11x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-x^{1}-12)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

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

$$\frac{\left(x^{2}-x^{1}-12\right)\times 11x^{1-1}-\left(11x^{1}-2\right)\left(2x^{2-1}-x^{1-1}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-x^{1}-12\right)\times 11x^{0}-\left(11x^{1}-2\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

x^{2}-x^{1}-12 ni 11x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 11x^{0}-x^{1}\times 11x^{0}-12\times 11x^{0}-\left(11x^{1}-2\right)\left(2x^{1}-x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

11x^{1}-2 ni 2x^{1}-x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 11x^{0}-x^{1}\times 11x^{0}-12\times 11x^{0}-\left(11x^{1}\times 2x^{1}+11x^{1}\left(-1\right)x^{0}-2\times 2x^{1}-2\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

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

$$\frac{11x^{2}-11x^{1}-12\times 11x^{0}-\left(11\times 2x^{1+1}+11\left(-1\right)x^{1}-2\times 2x^{1}-2\left(-1\right)x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

Qisqartirish.

$$\frac{11x^{2}-11x^{1}-132x^{0}-\left(22x^{2}-11x^{1}-4x^{1}+2x^{0}\right)}{\left(x^{2}-x^{1}-12\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-11x^{2}+4x^{1}-134x^{0}}{\left(x^{2}-x^{1}-12\right)^{2}}$$

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

$$\frac{-11x^{2}+4x-134x^{0}}{\left(x^{2}-x-12\right)^{2}}$$

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

$$\frac{-11x^{2}+4x-134}{\left(x^{2}-x-12\right)^{2}}$$