3/2x-5-4/x-3 eching

$$\frac{ 3 }{ 2x-5 } - \frac{ 4 }{ x-3 }$$

Baholash

$$\frac{11-5x}{\left(x-3\right)\left(2x-5\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2x-5 va x-3 ning eng kichik umumiy karralisi \left(x-3\right)\left(2x-5\right). \frac{3}{2x-5} ni \frac{x-3}{x-3} marotabaga ko'paytirish. \frac{4}{x-3} ni \frac{2x-5}{2x-5} marotabaga ko'paytirish.

$$\frac{3\left(x-3\right)}{\left(x-3\right)\left(2x-5\right)}-\frac{4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)}$$

\frac{3\left(x-3\right)}{\left(x-3\right)\left(2x-5\right)} va \frac{4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{3\left(x-3\right)-4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)}$$

3\left(x-3\right)-4\left(2x-5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{3x-9-8x+20}{\left(x-3\right)\left(2x-5\right)}$$

3x-9-8x+20 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-5x+11}{\left(x-3\right)\left(2x-5\right)}$$

\left(x-3\right)\left(2x-5\right) ni kengaytirish.

$$\frac{-5x+11}{2x^{2}-11x+15}$$

x ga nisbatan hosilani topish

$$\frac{2\left(\left(5x-11\right)^{2}-6\right)}{5\left(\left(x-3\right)\left(2x-5\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2x-5 va x-3 ning eng kichik umumiy karralisi \left(x-3\right)\left(2x-5\right). \frac{3}{2x-5} ni \frac{x-3}{x-3} marotabaga ko'paytirish. \frac{4}{x-3} ni \frac{2x-5}{2x-5} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x-3\right)}{\left(x-3\right)\left(2x-5\right)}-\frac{4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)})$$

\frac{3\left(x-3\right)}{\left(x-3\right)\left(2x-5\right)} va \frac{4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\left(x-3\right)-4\left(2x-5\right)}{\left(x-3\right)\left(2x-5\right)})$$

3\left(x-3\right)-4\left(2x-5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x-9-8x+20}{\left(x-3\right)\left(2x-5\right)})$$

3x-9-8x+20 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x+11}{\left(x-3\right)\left(2x-5\right)})$$

x-3 ifodaning har bir elementini 2x-5 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x+11}{2x^{2}-5x-6x+15})$$

-11x ni olish uchun -5x va -6x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-5x+11}{2x^{2}-11x+15})$$

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

$$\frac{\left(2x^{2}-11x^{1}+15\right)\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{1}+11)-\left(-5x^{1}+11\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}-11x^{1}+15)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

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

$$\frac{\left(2x^{2}-11x^{1}+15\right)\left(-5\right)x^{1-1}-\left(-5x^{1}+11\right)\left(2\times 2x^{2-1}-11x^{1-1}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Qisqartirish.

$$\frac{\left(2x^{2}-11x^{1}+15\right)\left(-5\right)x^{0}-\left(-5x^{1}+11\right)\left(4x^{1}-11x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

2x^{2}-11x^{1}+15 ni -5x^{0} marotabaga ko'paytirish.

$$\frac{2x^{2}\left(-5\right)x^{0}-11x^{1}\left(-5\right)x^{0}+15\left(-5\right)x^{0}-\left(-5x^{1}+11\right)\left(4x^{1}-11x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

-5x^{1}+11 ni 4x^{1}-11x^{0} marotabaga ko'paytirish.

$$\frac{2x^{2}\left(-5\right)x^{0}-11x^{1}\left(-5\right)x^{0}+15\left(-5\right)x^{0}-\left(-5x^{1}\times 4x^{1}-5x^{1}\left(-11\right)x^{0}+11\times 4x^{1}+11\left(-11\right)x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

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

$$\frac{2\left(-5\right)x^{2}-11\left(-5\right)x^{1}+15\left(-5\right)x^{0}-\left(-5\times 4x^{1+1}-5\left(-11\right)x^{1}+11\times 4x^{1}+11\left(-11\right)x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

Qisqartirish.

$$\frac{-10x^{2}+55x^{1}-75x^{0}-\left(-20x^{2}+55x^{1}+44x^{1}-121x^{0}\right)}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{10x^{2}-44x^{1}+46x^{0}}{\left(2x^{2}-11x^{1}+15\right)^{2}}$$

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

$$\frac{10x^{2}-44x+46x^{0}}{\left(2x^{2}-11x+15\right)^{2}}$$

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

$$\frac{10x^{2}-44x+46\times 1}{\left(2x^{2}-11x+15\right)^{2}}$$

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

$$\frac{10x^{2}-44x+46}{\left(2x^{2}-11x+15\right)^{2}}$$