1/x+1/x-47 eching

$$\frac{ 1 }{ x } + \frac{ 1 }{ x-47 }$$

Baholash

$$\frac{2x-47}{x\left(x-47\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va x-47 ning eng kichik umumiy karralisi x\left(x-47\right). \frac{1}{x} ni \frac{x-47}{x-47} marotabaga ko'paytirish. \frac{1}{x-47} ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{x-47}{x\left(x-47\right)}+\frac{x}{x\left(x-47\right)}$$

\frac{x-47}{x\left(x-47\right)} va \frac{x}{x\left(x-47\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{x-47+x}{x\left(x-47\right)}$$

x-47+x kabi iboralarga o‘xshab birlashtiring.

$$\frac{2x-47}{x\left(x-47\right)}$$

x\left(x-47\right) ni kengaytirish.

$$\frac{2x-47}{x^{2}-47x}$$

x ga nisbatan hosilani topish

$$\frac{-2x^{2}+94x-2209}{\left(x\left(x-47\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x va x-47 ning eng kichik umumiy karralisi x\left(x-47\right). \frac{1}{x} ni \frac{x-47}{x-47} marotabaga ko'paytirish. \frac{1}{x-47} ni \frac{x}{x} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-47}{x\left(x-47\right)}+\frac{x}{x\left(x-47\right)})$$

\frac{x-47}{x\left(x-47\right)} va \frac{x}{x\left(x-47\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-47+x}{x\left(x-47\right)})$$

x-47+x kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-47}{x\left(x-47\right)})$$

x ga x-47 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-47}{x^{2}-47x})$$

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

$$\frac{\left(x^{2}-47x^{1}\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}-47)-\left(2x^{1}-47\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-47x^{1})}{\left(x^{2}-47x^{1}\right)^{2}}$$

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

$$\frac{\left(x^{2}-47x^{1}\right)\times 2x^{1-1}-\left(2x^{1}-47\right)\left(2x^{2-1}-47x^{1-1}\right)}{\left(x^{2}-47x^{1}\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-47x^{1}\right)\times 2x^{0}-\left(2x^{1}-47\right)\left(2x^{1}-47x^{0}\right)}{\left(x^{2}-47x^{1}\right)^{2}}$$

x^{2}-47x^{1} ni 2x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 2x^{0}-47x^{1}\times 2x^{0}-\left(2x^{1}-47\right)\left(2x^{1}-47x^{0}\right)}{\left(x^{2}-47x^{1}\right)^{2}}$$

2x^{1}-47 ni 2x^{1}-47x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 2x^{0}-47x^{1}\times 2x^{0}-\left(2x^{1}\times 2x^{1}+2x^{1}\left(-47\right)x^{0}-47\times 2x^{1}-47\left(-47\right)x^{0}\right)}{\left(x^{2}-47x^{1}\right)^{2}}$$

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

$$\frac{2x^{2}-47\times 2x^{1}-\left(2\times 2x^{1+1}+2\left(-47\right)x^{1}-47\times 2x^{1}-47\left(-47\right)x^{0}\right)}{\left(x^{2}-47x^{1}\right)^{2}}$$

Qisqartirish.

$$\frac{2x^{2}-94x^{1}-\left(4x^{2}-94x^{1}-94x^{1}+2209x^{0}\right)}{\left(x^{2}-47x^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-2x^{2}+94x^{1}-2209x^{0}}{\left(x^{2}-47x^{1}\right)^{2}}$$

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

$$\frac{-2x^{2}+94x-2209x^{0}}{\left(x^{2}-47x\right)^{2}}$$

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

$$\frac{-2x^{2}+94x-2209}{\left(x^{2}-47x\right)^{2}}$$