5/(x-3)-3/(x-2) eching

$$\frac { 5 } { ( x - 3 ) } - \frac { 3 } { ( x - 2 ) }$$

Baholash

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

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-3 va x-2 ning eng kichik umumiy karralisi \left(x-3\right)\left(x-2\right). \frac{5}{x-3} ni \frac{x-2}{x-2} marotabaga ko'paytirish. \frac{3}{x-2} ni \frac{x-3}{x-3} marotabaga ko'paytirish.

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

\frac{5\left(x-2\right)}{\left(x-3\right)\left(x-2\right)} va \frac{3\left(x-3\right)}{\left(x-3\right)\left(x-2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

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

$$\frac{5x-10-3x+9}{\left(x-3\right)\left(x-2\right)}$$

5x-10-3x+9 kabi iboralarga o‘xshab birlashtiring.

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

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

$$\frac{2x-1}{x^{2}-5x+6}$$

x ga nisbatan hosilani topish

$$\frac{7+2x-2x^{2}}{x^{4}-10x^{3}+37x^{2}-60x+36}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-3 va x-2 ning eng kichik umumiy karralisi \left(x-3\right)\left(x-2\right). \frac{5}{x-3} ni \frac{x-2}{x-2} marotabaga ko'paytirish. \frac{3}{x-2} ni \frac{x-3}{x-3} marotabaga ko'paytirish.

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

\frac{5\left(x-2\right)}{\left(x-3\right)\left(x-2\right)} va \frac{3\left(x-3\right)}{\left(x-3\right)\left(x-2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-10-3x+9}{\left(x-3\right)\left(x-2\right)})$$

5x-10-3x+9 kabi iboralarga o‘xshab birlashtiring.

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

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

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

-5x ni olish uchun -2x va -3x ni birlashtirish.

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

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

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

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

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

Qisqartirish.

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

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

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

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

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

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

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

Qisqartirish.

$$\frac{2x^{2}-10x^{1}+12x^{0}-\left(4x^{2}-10x^{1}-2x^{1}+5x^{0}\right)}{\left(x^{2}-5x^{1}+6\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-2x^{2}+2x^{1}+7x^{0}}{\left(x^{2}-5x^{1}+6\right)^{2}}$$

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

$$\frac{-2x^{2}+2x+7x^{0}}{\left(x^{2}-5x+6\right)^{2}}$$

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

$$\frac{-2x^{2}+2x+7\times 1}{\left(x^{2}-5x+6\right)^{2}}$$

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

$$\frac{-2x^{2}+2x+7}{\left(x^{2}-5x+6\right)^{2}}$$