x/x^2+10x+24-4/x^2+6x+8 eching

$$\frac { x } { x ^ { 2 } + 10 x + 24 } - \frac { 4 } { x ^ { 2 } + 6 x + 8 }$$

Baholash

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

Qisqa yechim qadamlari

Faktor: x^{2}+10x+24. Faktor: x^{2}+6x+8.

$$\frac{x}{\left(x+4\right)\left(x+6\right)}-\frac{4}{\left(x+2\right)\left(x+4\right)}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x+4\right)\left(x+6\right) va \left(x+2\right)\left(x+4\right) ning eng kichik umumiy karralisi \left(x+2\right)\left(x+4\right)\left(x+6\right). \frac{x}{\left(x+4\right)\left(x+6\right)} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{4}{\left(x+2\right)\left(x+4\right)} ni \frac{x+6}{x+6} marotabaga ko'paytirish.

$$\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}-\frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} va \frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{x\left(x+2\right)-4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

x\left(x+2\right)-4\left(x+6\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x^{2}+2x-4x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

x^{2}+2x-4x-24 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\left(x-6\right)\left(x+4\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}$$

Surat va maxrajdagi ikkala x+4 ni qisqartiring.

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

\left(x+2\right)\left(x+6\right) ni kengaytirish.

$$\frac{x-6}{x^{2}+8x+12}$$

x ga nisbatan hosilani topish

$$\frac{60+12x-x^{2}}{x^{4}+16x^{3}+88x^{2}+192x+144}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: x^{2}+10x+24. Faktor: x^{2}+6x+8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x+4\right)\left(x+6\right)}-\frac{4}{\left(x+2\right)\left(x+4\right)})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x+4\right)\left(x+6\right) va \left(x+2\right)\left(x+4\right) ning eng kichik umumiy karralisi \left(x+2\right)\left(x+4\right)\left(x+6\right). \frac{x}{\left(x+4\right)\left(x+6\right)} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{4}{\left(x+2\right)\left(x+4\right)} ni \frac{x+6}{x+6} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)}-\frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

\frac{x\left(x+2\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} va \frac{4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\left(x+2\right)-4\left(x+6\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

x\left(x+2\right)-4\left(x+6\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+2x-4x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

x^{2}+2x-4x-24 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

\frac{x^{2}-2x-24}{\left(x+2\right)\left(x+4\right)\left(x+6\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-6\right)\left(x+4\right)}{\left(x+2\right)\left(x+4\right)\left(x+6\right)})$$

Surat va maxrajdagi ikkala x+4 ni qisqartiring.

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

x+2 ga x+6 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-6}{x^{2}+8x+12})$$

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

$$\frac{\left(x^{2}+8x^{1}+12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-6)-\left(x^{1}-6\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+8x^{1}+12)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

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

$$\frac{\left(x^{2}+8x^{1}+12\right)x^{1-1}-\left(x^{1}-6\right)\left(2x^{2-1}+8x^{1-1}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}+8x^{1}+12\right)x^{0}-\left(x^{1}-6\right)\left(2x^{1}+8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

x^{2}+8x^{1}+12 ni x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}x^{0}+8x^{1}x^{0}+12x^{0}-\left(x^{1}-6\right)\left(2x^{1}+8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

x^{1}-6 ni 2x^{1}+8x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}x^{0}+8x^{1}x^{0}+12x^{0}-\left(x^{1}\times 2x^{1}+x^{1}\times 8x^{0}-6\times 2x^{1}-6\times 8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

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

$$\frac{x^{2}+8x^{1}+12x^{0}-\left(2x^{1+1}+8x^{1}-6\times 2x^{1}-6\times 8x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

Qisqartirish.

$$\frac{x^{2}+8x^{1}+12x^{0}-\left(2x^{2}+8x^{1}-12x^{1}-48x^{0}\right)}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-x^{2}+12x^{1}+60x^{0}}{\left(x^{2}+8x^{1}+12\right)^{2}}$$

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

$$\frac{-x^{2}+12x+60x^{0}}{\left(x^{2}+8x+12\right)^{2}}$$

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

$$\frac{-x^{2}+12x+60\times 1}{\left(x^{2}+8x+12\right)^{2}}$$

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

$$\frac{-x^{2}+12x+60}{\left(x^{2}+8x+12\right)^{2}}$$