x+4+1/x-2 eching

$$x + 4 + \frac { 1 } { x - 2 }$$

Baholash

$$\frac{x^{2}+2x-7}{x-2}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+4 ni \frac{x-2}{x-2} marotabaga ko'paytirish.

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

\frac{\left(x+4\right)\left(x-2\right)}{x-2} va \frac{1}{x-2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(x+4\right)\left(x-2\right)+1 ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}-2x+4x-8+1}{x-2}$$

x^{2}-2x+4x-8+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{2}+2x-7}{x-2}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+4 ni \frac{x-2}{x-2} marotabaga ko'paytirish.

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

\frac{\left(x+4\right)\left(x-2\right)}{x-2} va \frac{1}{x-2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(x+4\right)\left(x-2\right)+1 ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}-2x+4x-8+1}{x-2})$$

x^{2}-2x+4x-8+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+2x-7}{x-2})$$

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

$$\frac{\left(x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+2x^{1}-7)-\left(x^{2}+2x^{1}-7\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-2)}{\left(x^{1}-2\right)^{2}}$$

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

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

Qisqartirish.

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

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

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

x^{2}+2x^{1}-7 ni x^{0} marotabaga ko'paytirish.

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

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

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

Qisqartirish.

$$\frac{2x^{2}+2x^{1}-4x^{1}-4x^{0}-\left(x^{2}+2x^{1}-7x^{0}\right)}{\left(x^{1}-2\right)^{2}}$$

O'xshash hadlarni birlashtirish.

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

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

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

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

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

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

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