(x+2)-4/x-1 eching

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

Baholash

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

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+2 ni \frac{x-1}{x-1} marotabaga ko'paytirish.

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

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

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

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

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

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

$$\frac{x^{2}+x-6}{x-1}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+2 ni \frac{x-1}{x-1} marotabaga ko'paytirish.

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

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+x-6}{x-1})$$

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

$$\frac{\left(x^{1}-1\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+x^{1}-6)-\left(x^{2}+x^{1}-6\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-1)}{\left(x^{1}-1\right)^{2}}$$

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

$$\frac{\left(x^{1}-1\right)\left(2x^{2-1}+x^{1-1}\right)-\left(x^{2}+x^{1}-6\right)x^{1-1}}{\left(x^{1}-1\right)^{2}}$$

Qisqartirish.

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

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

$$\frac{x^{1}\times 2x^{1}+x^{1}x^{0}-2x^{1}-x^{0}-\left(x^{2}+x^{1}-6\right)x^{0}}{\left(x^{1}-1\right)^{2}}$$

x^{2}+x^{1}-6 ni x^{0} marotabaga ko'paytirish.

$$\frac{x^{1}\times 2x^{1}+x^{1}x^{0}-2x^{1}-x^{0}-\left(x^{2}x^{0}+x^{1}x^{0}-6x^{0}\right)}{\left(x^{1}-1\right)^{2}}$$

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

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

Qisqartirish.

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

O'xshash hadlarni birlashtirish.

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

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

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

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

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

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

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