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

$$\frac { 4 } { x - 7 } + \frac { 3 } { x + 2 }$$

Baholash

$$\frac{7x-13}{\left(x-7\right)\left(x+2\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-7 va x+2 ning eng kichik umumiy karralisi \left(x-7\right)\left(x+2\right). \frac{4}{x-7} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{3}{x+2} ni \frac{x-7}{x-7} marotabaga ko'paytirish.

$$\frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)}+\frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)}$$

\frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)} va \frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{4\left(x+2\right)+3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)}$$

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

$$\frac{4x+8+3x-21}{\left(x-7\right)\left(x+2\right)}$$

4x+8+3x-21 kabi iboralarga o‘xshab birlashtiring.

$$\frac{7x-13}{\left(x-7\right)\left(x+2\right)}$$

\left(x-7\right)\left(x+2\right) ni kengaytirish.

$$\frac{7x-13}{x^{2}-5x-14}$$

x ga nisbatan hosilani topish

$$\frac{-7x^{2}+26x-163}{\left(\left(x-7\right)\left(x+2\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-7 va x+2 ning eng kichik umumiy karralisi \left(x-7\right)\left(x+2\right). \frac{4}{x-7} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{3}{x+2} ni \frac{x-7}{x-7} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)}+\frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)})$$

\frac{4\left(x+2\right)}{\left(x-7\right)\left(x+2\right)} va \frac{3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\left(x+2\right)+3\left(x-7\right)}{\left(x-7\right)\left(x+2\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+8+3x-21}{\left(x-7\right)\left(x+2\right)})$$

4x+8+3x-21 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-13}{\left(x-7\right)\left(x+2\right)})$$

x-7 ifodaning har bir elementini x+2 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-13}{x^{2}+2x-7x-14})$$

-5x ni olish uchun 2x va -7x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-13}{x^{2}-5x-14})$$

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

$$\frac{\left(x^{2}-5x^{1}-14\right)\frac{\mathrm{d}}{\mathrm{d}x}(7x^{1}-13)-\left(7x^{1}-13\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-5x^{1}-14)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

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

$$\frac{\left(x^{2}-5x^{1}-14\right)\times 7x^{1-1}-\left(7x^{1}-13\right)\left(2x^{2-1}-5x^{1-1}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-5x^{1}-14\right)\times 7x^{0}-\left(7x^{1}-13\right)\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

x^{2}-5x^{1}-14 ni 7x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 7x^{0}-5x^{1}\times 7x^{0}-14\times 7x^{0}-\left(7x^{1}-13\right)\left(2x^{1}-5x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

7x^{1}-13 ni 2x^{1}-5x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 7x^{0}-5x^{1}\times 7x^{0}-14\times 7x^{0}-\left(7x^{1}\times 2x^{1}+7x^{1}\left(-5\right)x^{0}-13\times 2x^{1}-13\left(-5\right)x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

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

$$\frac{7x^{2}-5\times 7x^{1}-14\times 7x^{0}-\left(7\times 2x^{1+1}+7\left(-5\right)x^{1}-13\times 2x^{1}-13\left(-5\right)x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

Qisqartirish.

$$\frac{7x^{2}-35x^{1}-98x^{0}-\left(14x^{2}-35x^{1}-26x^{1}+65x^{0}\right)}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-7x^{2}+26x^{1}-163x^{0}}{\left(x^{2}-5x^{1}-14\right)^{2}}$$

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

$$\frac{-7x^{2}+26x-163x^{0}}{\left(x^{2}-5x-14\right)^{2}}$$

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

$$\frac{-7x^{2}+26x-163}{\left(x^{2}-5x-14\right)^{2}}$$