2/x-5-5/x+3 eching

$$\frac { 2 } { x - 5 } - \frac { 5 } { x + 3 }$$

Baholash

$$\frac{31-3x}{\left(x-5\right)\left(x+3\right)}$$

Qisqa yechim qadamlari

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

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

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

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

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

$$\frac{2x+6-5x+25}{\left(x-5\right)\left(x+3\right)}$$

2x+6-5x+25 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-3x+31}{\left(x-5\right)\left(x+3\right)}$$

\left(x-5\right)\left(x+3\right) ni kengaytirish.

$$\frac{-3x+31}{x^{2}-2x-15}$$

x ga nisbatan hosilani topish

$$\frac{3x^{2}-62x+107}{x^{4}-4x^{3}-26x^{2}+60x+225}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x+6-5x+25}{\left(x-5\right)\left(x+3\right)})$$

2x+6-5x+25 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3x+31}{\left(x-5\right)\left(x+3\right)})$$

x-5 ifodaning har bir elementini x+3 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3x+31}{x^{2}+3x-5x-15})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3x+31}{x^{2}-2x-15})$$

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

$$\frac{\left(x^{2}-2x^{1}-15\right)\frac{\mathrm{d}}{\mathrm{d}x}(-3x^{1}+31)-\left(-3x^{1}+31\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-2x^{1}-15)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

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

$$\frac{\left(x^{2}-2x^{1}-15\right)\left(-3\right)x^{1-1}-\left(-3x^{1}+31\right)\left(2x^{2-1}-2x^{1-1}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-2x^{1}-15\right)\left(-3\right)x^{0}-\left(-3x^{1}+31\right)\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

x^{2}-2x^{1}-15 ni -3x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\left(-3\right)x^{0}-2x^{1}\left(-3\right)x^{0}-15\left(-3\right)x^{0}-\left(-3x^{1}+31\right)\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

-3x^{1}+31 ni 2x^{1}-2x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\left(-3\right)x^{0}-2x^{1}\left(-3\right)x^{0}-15\left(-3\right)x^{0}-\left(-3x^{1}\times 2x^{1}-3x^{1}\left(-2\right)x^{0}+31\times 2x^{1}+31\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

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

$$\frac{-3x^{2}-2\left(-3\right)x^{1}-15\left(-3\right)x^{0}-\left(-3\times 2x^{1+1}-3\left(-2\right)x^{1}+31\times 2x^{1}+31\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

Qisqartirish.

$$\frac{-3x^{2}+6x^{1}+45x^{0}-\left(-6x^{2}+6x^{1}+62x^{1}-62x^{0}\right)}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{3x^{2}-62x^{1}+107x^{0}}{\left(x^{2}-2x^{1}-15\right)^{2}}$$

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

$$\frac{3x^{2}-62x+107x^{0}}{\left(x^{2}-2x-15\right)^{2}}$$

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

$$\frac{3x^{2}-62x+107\times 1}{\left(x^{2}-2x-15\right)^{2}}$$

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

$$\frac{3x^{2}-62x+107}{\left(x^{2}-2x-15\right)^{2}}$$