1/x-3-2/x^2-9= eching

$$\frac { 1 } { x - 3 } - \frac { 2 } { x ^ { 2 } - 9 } =$$

Baholash

$$\frac{x+1}{x^{2}-9}$$

Qisqa yechim qadamlari

Faktor: x^{2}-9.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-3 va \left(x-3\right)\left(x+3\right) ning eng kichik umumiy karralisi \left(x-3\right)\left(x+3\right). \frac{1}{x-3} ni \frac{x+3}{x+3} marotabaga ko'paytirish.

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

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

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

x+3-2 kabi iboralarga o‘xshab birlashtiring.

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

\left(x-3\right)\left(x+3\right) ni kengaytirish.

$$\frac{x+1}{x^{2}-9}$$

x ga nisbatan hosilani topish

$$\frac{-x^{2}-2x-9}{\left(x^{2}-9\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: x^{2}-9.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x-3 va \left(x-3\right)\left(x+3\right) ning eng kichik umumiy karralisi \left(x-3\right)\left(x+3\right). \frac{1}{x-3} ni \frac{x+3}{x+3} marotabaga ko'paytirish.

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

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

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

x+3-2 kabi iboralarga o‘xshab birlashtiring.

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

Hisoblang: \left(x-3\right)\left(x+3\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 3 kvadratini chiqarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+1}{x^{2}-9})$$

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

$$\frac{\left(x^{2}-9\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+1)-\left(x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-9)}{\left(x^{2}-9\right)^{2}}$$

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

$$\frac{\left(x^{2}-9\right)x^{1-1}-\left(x^{1}+1\right)\times 2x^{2-1}}{\left(x^{2}-9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{2}-9\right)x^{0}-\left(x^{1}+1\right)\times 2x^{1}}{\left(x^{2}-9\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{2}x^{0}-9x^{0}-\left(x^{1}\times 2x^{1}+2x^{1}\right)}{\left(x^{2}-9\right)^{2}}$$

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

$$\frac{x^{2}-9x^{0}-\left(2x^{1+1}+2x^{1}\right)}{\left(x^{2}-9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{x^{2}-9x^{0}-\left(2x^{2}+2x^{1}\right)}{\left(x^{2}-9\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{x^{2}-9x^{0}-2x^{2}-2x^{1}}{\left(x^{2}-9\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(1-2\right)x^{2}-9x^{0}-2x^{1}}{\left(x^{2}-9\right)^{2}}$$

1 dan 2 ni ayirish.

$$\frac{-x^{2}-9x^{0}-2x^{1}}{\left(x^{2}-9\right)^{2}}$$

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

$$\frac{-x^{2}-9x^{0}-2x}{\left(x^{2}-9\right)^{2}}$$

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

$$\frac{-x^{2}-9-2x}{\left(x^{2}-9\right)^{2}}$$