4*6/x^2-4x+3-3/3-x-4/x-1 eching

$$\frac { 4 \times 6 } { x ^ { 2 } - 4 x + 3 } - \frac { 3 } { 3 - x } - \frac { 4 } { x - 1 }$$

Baholash

$$\frac{x-33}{\left(3-x\right)\left(x-1\right)}$$

Qisqa yechim qadamlari

24 hosil qilish uchun 4 va 6 ni ko'paytirish.

$$\frac{24}{x^{2}-4x+3}-\frac{3}{3-x}-\frac{4}{x-1}$$

Faktor: x^{2}-4x+3.

$$\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3}{3-x}-\frac{4}{x-1}$$

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

$$\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

\frac{24}{\left(x-3\right)\left(x-1\right)} va \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{24-3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

24-3\left(-1\right)\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{24+3x-3}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

24+3x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-3\right)\left(x-1\right) va x-1 ning eng kichik umumiy karralisi \left(x-3\right)\left(x-1\right). \frac{4}{x-1} ni \frac{x-3}{x-3} marotabaga ko'paytirish.

$$\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}$$

\frac{21+3x}{\left(x-3\right)\left(x-1\right)} va \frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{21+3x-4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)}$$

21+3x-4\left(x-3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{21+3x-4x+12}{\left(x-3\right)\left(x-1\right)}$$

21+3x-4x+12 kabi iboralarga o‘xshab birlashtiring.

$$\frac{33-x}{\left(x-3\right)\left(x-1\right)}$$

\left(x-3\right)\left(x-1\right) ni kengaytirish.

$$\frac{33-x}{x^{2}-4x+3}$$

x ga nisbatan hosilani topish

$$\frac{x^{2}-66x+129}{x^{4}-8x^{3}+22x^{2}-24x+9}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

24 hosil qilish uchun 4 va 6 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{x^{2}-4x+3}-\frac{3}{3-x}-\frac{4}{x-1})$$

Faktor: x^{2}-4x+3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3}{3-x}-\frac{4}{x-1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{\left(x-3\right)\left(x-1\right)}-\frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

\frac{24}{\left(x-3\right)\left(x-1\right)} va \frac{3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24-3\left(-1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

24-3\left(-1\right)\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24+3x-3}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

24+3x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4}{x-1})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-3\right)\left(x-1\right) va x-1 ning eng kichik umumiy karralisi \left(x-3\right)\left(x-1\right). \frac{4}{x-1} ni \frac{x-3}{x-3} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x}{\left(x-3\right)\left(x-1\right)}-\frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)})$$

\frac{21+3x}{\left(x-3\right)\left(x-1\right)} va \frac{4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x-4\left(x-3\right)}{\left(x-3\right)\left(x-1\right)})$$

21+3x-4\left(x-3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21+3x-4x+12}{\left(x-3\right)\left(x-1\right)})$$

21+3x-4x+12 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33-x}{\left(x-3\right)\left(x-1\right)})$$

x-3 ga x-1 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{33-x}{x^{2}-4x+3})$$

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

$$\frac{\left(x^{2}-4x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}+33)-\left(-x^{1}+33\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x^{1}+3)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

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

$$\frac{\left(x^{2}-4x^{1}+3\right)\left(-1\right)x^{1-1}-\left(-x^{1}+33\right)\left(2x^{2-1}-4x^{1-1}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-4x^{1}+3\right)\left(-1\right)x^{0}-\left(-x^{1}+33\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

x^{2}-4x^{1}+3 ni -x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\left(-1\right)x^{0}-4x^{1}\left(-1\right)x^{0}+3\left(-1\right)x^{0}-\left(-x^{1}+33\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

-x^{1}+33 ni 2x^{1}-4x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\left(-1\right)x^{0}-4x^{1}\left(-1\right)x^{0}+3\left(-1\right)x^{0}-\left(-x^{1}\times 2x^{1}-x^{1}\left(-4\right)x^{0}+33\times 2x^{1}+33\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

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

$$\frac{-x^{2}-4\left(-1\right)x^{1}+3\left(-1\right)x^{0}-\left(-2x^{1+1}-\left(-4x^{1}\right)+33\times 2x^{1}+33\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

Qisqartirish.

$$\frac{-x^{2}+4x^{1}-3x^{0}-\left(-2x^{2}+4x^{1}+66x^{1}-132x^{0}\right)}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{x^{2}-66x^{1}+129x^{0}}{\left(x^{2}-4x^{1}+3\right)^{2}}$$

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

$$\frac{x^{2}-66x+129x^{0}}{\left(x^{2}-4x+3\right)^{2}}$$

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

$$\frac{x^{2}-66x+129\times 1}{\left(x^{2}-4x+3\right)^{2}}$$

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

$$\frac{x^{2}-66x+129}{\left(x^{2}-4x+3\right)^{2}}$$