8x/2x-2+3 eching

$$\frac { 8 x } { 2 x - 2 } + 3$$

Baholash

$$\frac{7x-3}{x-1}$$

Qisqa yechim qadamlari

\frac{8x}{2x-2} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{8x}{2\left(x-1\right)}+3$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{4x}{x-1}+3$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 ni \frac{x-1}{x-1} marotabaga ko'paytirish.

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

\frac{4x}{x-1} va \frac{3\left(x-1\right)}{x-1} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

4x+3\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{4x+3x-3}{x-1}$$

4x+3x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{7x-3}{x-1}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

\frac{8x}{2x-2} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8x}{2\left(x-1\right)}+3)$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x}{x-1}+3)$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3 ni \frac{x-1}{x-1} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x}{x-1}+\frac{3\left(x-1\right)}{x-1})$$

\frac{4x}{x-1} va \frac{3\left(x-1\right)}{x-1} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+3\left(x-1\right)}{x-1})$$

4x+3\left(x-1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x+3x-3}{x-1})$$

4x+3x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7x-3}{x-1})$$

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

$$\frac{\left(x^{1}-1\right)\frac{\mathrm{d}}{\mathrm{d}x}(7x^{1}-3)-\left(7x^{1}-3\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-1)}{\left(x^{1}-1\right)^{2}}$$

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

$$\frac{\left(x^{1}-1\right)\times 7x^{1-1}-\left(7x^{1}-3\right)x^{1-1}}{\left(x^{1}-1\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}-1\right)\times 7x^{0}-\left(7x^{1}-3\right)x^{0}}{\left(x^{1}-1\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\times 7x^{0}-7x^{0}-\left(7x^{1}x^{0}-3x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

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

$$\frac{7x^{1}-7x^{0}-\left(7x^{1}-3x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{7x^{1}-7x^{0}-7x^{1}-\left(-3x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(7-7\right)x^{1}+\left(-7-\left(-3\right)\right)x^{0}}{\left(x^{1}-1\right)^{2}}$$

7 dan 7 ni va -7 dan -3 ni ayiring.

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

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

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

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

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