5x/x^2-4x-21-3/x-7+4/x+3 eching

$$\frac { 5 x } { x ^ { 2 } - 4 x - 21 } - \frac { 3 } { x - 7 } + \frac { 4 } { x + 3 }$$

Baholash

$$\frac{6x-37}{\left(x-7\right)\left(x+3\right)}$$

Qisqa yechim qadamlari

Faktor: x^{2}-4x-21.

$$\frac{5x}{\left(x-7\right)\left(x+3\right)}-\frac{3}{x-7}+\frac{4}{x+3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-7\right)\left(x+3\right) va x-7 ning eng kichik umumiy karralisi \left(x-7\right)\left(x+3\right). \frac{3}{x-7} ni \frac{x+3}{x+3} marotabaga ko'paytirish.

$$\frac{5x}{\left(x-7\right)\left(x+3\right)}-\frac{3\left(x+3\right)}{\left(x-7\right)\left(x+3\right)}+\frac{4}{x+3}$$

\frac{5x}{\left(x-7\right)\left(x+3\right)} va \frac{3\left(x+3\right)}{\left(x-7\right)\left(x+3\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{5x-3\left(x+3\right)}{\left(x-7\right)\left(x+3\right)}+\frac{4}{x+3}$$

5x-3\left(x+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{5x-3x-9}{\left(x-7\right)\left(x+3\right)}+\frac{4}{x+3}$$

5x-3x-9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{2x-9}{\left(x-7\right)\left(x+3\right)}+\frac{4}{x+3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-7\right)\left(x+3\right) va x+3 ning eng kichik umumiy karralisi \left(x-7\right)\left(x+3\right). \frac{4}{x+3} ni \frac{x-7}{x-7} marotabaga ko'paytirish.

$$\frac{2x-9}{\left(x-7\right)\left(x+3\right)}+\frac{4\left(x-7\right)}{\left(x-7\right)\left(x+3\right)}$$

\frac{2x-9}{\left(x-7\right)\left(x+3\right)} va \frac{4\left(x-7\right)}{\left(x-7\right)\left(x+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{2x-9+4\left(x-7\right)}{\left(x-7\right)\left(x+3\right)}$$

2x-9+4\left(x-7\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2x-9+4x-28}{\left(x-7\right)\left(x+3\right)}$$

2x-9+4x-28 kabi iboralarga o‘xshab birlashtiring.

$$\frac{6x-37}{\left(x-7\right)\left(x+3\right)}$$

\left(x-7\right)\left(x+3\right) ni kengaytirish.

$$\frac{6x-37}{x^{2}-4x-21}$$

x ga nisbatan hosilani topish

$$\frac{2\left(-3x^{2}+37x-137\right)}{\left(\left(x-7\right)\left(x+3\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: x^{2}-4x-21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{\left(x-7\right)\left(x+3\right)}-\frac{3}{x-7}+\frac{4}{x+3})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-7\right)\left(x+3\right) va x-7 ning eng kichik umumiy karralisi \left(x-7\right)\left(x+3\right). \frac{3}{x-7} ni \frac{x+3}{x+3} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x}{\left(x-7\right)\left(x+3\right)}-\frac{3\left(x+3\right)}{\left(x-7\right)\left(x+3\right)}+\frac{4}{x+3})$$

\frac{5x}{\left(x-7\right)\left(x+3\right)} va \frac{3\left(x+3\right)}{\left(x-7\right)\left(x+3\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-3\left(x+3\right)}{\left(x-7\right)\left(x+3\right)}+\frac{4}{x+3})$$

5x-3\left(x+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-3x-9}{\left(x-7\right)\left(x+3\right)}+\frac{4}{x+3})$$

5x-3x-9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-9}{\left(x-7\right)\left(x+3\right)}+\frac{4}{x+3})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-7\right)\left(x+3\right) va x+3 ning eng kichik umumiy karralisi \left(x-7\right)\left(x+3\right). \frac{4}{x+3} ni \frac{x-7}{x-7} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-9}{\left(x-7\right)\left(x+3\right)}+\frac{4\left(x-7\right)}{\left(x-7\right)\left(x+3\right)})$$

\frac{2x-9}{\left(x-7\right)\left(x+3\right)} va \frac{4\left(x-7\right)}{\left(x-7\right)\left(x+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-9+4\left(x-7\right)}{\left(x-7\right)\left(x+3\right)})$$

2x-9+4\left(x-7\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-9+4x-28}{\left(x-7\right)\left(x+3\right)})$$

2x-9+4x-28 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x-37}{\left(x-7\right)\left(x+3\right)})$$

x-7 ga x+3 ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x-37}{x^{2}-4x-21})$$

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

$$\frac{\left(x^{2}-4x^{1}-21\right)\frac{\mathrm{d}}{\mathrm{d}x}(6x^{1}-37)-\left(6x^{1}-37\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-4x^{1}-21)}{\left(x^{2}-4x^{1}-21\right)^{2}}$$

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

$$\frac{\left(x^{2}-4x^{1}-21\right)\times 6x^{1-1}-\left(6x^{1}-37\right)\left(2x^{2-1}-4x^{1-1}\right)}{\left(x^{2}-4x^{1}-21\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-4x^{1}-21\right)\times 6x^{0}-\left(6x^{1}-37\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}-21\right)^{2}}$$

x^{2}-4x^{1}-21 ni 6x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 6x^{0}-4x^{1}\times 6x^{0}-21\times 6x^{0}-\left(6x^{1}-37\right)\left(2x^{1}-4x^{0}\right)}{\left(x^{2}-4x^{1}-21\right)^{2}}$$

6x^{1}-37 ni 2x^{1}-4x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 6x^{0}-4x^{1}\times 6x^{0}-21\times 6x^{0}-\left(6x^{1}\times 2x^{1}+6x^{1}\left(-4\right)x^{0}-37\times 2x^{1}-37\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}-21\right)^{2}}$$

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

$$\frac{6x^{2}-4\times 6x^{1}-21\times 6x^{0}-\left(6\times 2x^{1+1}+6\left(-4\right)x^{1}-37\times 2x^{1}-37\left(-4\right)x^{0}\right)}{\left(x^{2}-4x^{1}-21\right)^{2}}$$

Qisqartirish.

$$\frac{6x^{2}-24x^{1}-126x^{0}-\left(12x^{2}-24x^{1}-74x^{1}+148x^{0}\right)}{\left(x^{2}-4x^{1}-21\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-6x^{2}+74x^{1}-274x^{0}}{\left(x^{2}-4x^{1}-21\right)^{2}}$$

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

$$\frac{-6x^{2}+74x-274x^{0}}{\left(x^{2}-4x-21\right)^{2}}$$

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

$$\frac{-6x^{2}+74x-274}{\left(x^{2}-4x-21\right)^{2}}$$