1/x^2-1-2/x^2+3x-4+1/x^2-2x-3 eching

$$\frac { 1 } { x ^ { 2 } - 1 } - \frac { 2 } { x ^ { 2 } + 3 x - 4 } + \frac { 1 } { x ^ { 2 } - 2 x - 3 }$$

Baholash

$$\frac{2\left(4x-5\right)}{\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)}$$

Qisqa yechim qadamlari

Faktor: x^{2}-1. Faktor: x^{2}+3x-4.

$$\frac{1}{\left(x-1\right)\left(x+1\right)}-\frac{2}{\left(x-1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-1\right)\left(x+1\right) va \left(x-1\right)\left(x+4\right) ning eng kichik umumiy karralisi \left(x-1\right)\left(x+1\right)\left(x+4\right). \frac{1}{\left(x-1\right)\left(x+1\right)} ni \frac{x+4}{x+4} marotabaga ko'paytirish. \frac{2}{\left(x-1\right)\left(x+4\right)} ni \frac{x+1}{x+1} marotabaga ko'paytirish.

$$\frac{x+4}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}-\frac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}$$

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

$$\frac{x+4-2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}$$

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

$$\frac{x+4-2x-2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}$$

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

$$\frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{x^{2}-2x-3}$$

Faktor: x^{2}-2x-3.

$$\frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{1}{\left(x-3\right)\left(x+1\right)}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-1\right)\left(x+1\right)\left(x+4\right) va \left(x-3\right)\left(x+1\right) ning eng kichik umumiy karralisi \left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right). \frac{-x+2}{\left(x-1\right)\left(x+1\right)\left(x+4\right)} ni \frac{x-3}{x-3} marotabaga ko'paytirish. \frac{1}{\left(x-3\right)\left(x+1\right)} ni \frac{\left(x-1\right)\left(x+4\right)}{\left(x-1\right)\left(x+4\right)} marotabaga ko'paytirish.

$$\frac{\left(-x+2\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}+\frac{\left(x-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}$$

\frac{\left(-x+2\right)\left(x-3\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} va \frac{\left(x-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right)}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}$$

\left(-x+2\right)\left(x-3\right)+\left(x-1\right)\left(x+4\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{-x^{2}+3x+2x-6+x^{2}+4x-x-4}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}$$

-x^{2}+3x+2x-6+x^{2}+4x-x-4 kabi iboralarga o‘xshab birlashtiring.

$$\frac{8x-10}{\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)}$$

\left(x-3\right)\left(x-1\right)\left(x+1\right)\left(x+4\right) ni kengaytirish.

$$\frac{8x-10}{x^{4}+x^{3}-13x^{2}-x+12}$$

x ga nisbatan hosilani topish

$$\frac{2\left(43-130x+67x^{2}+12x^{3}-12x^{4}\right)}{\left(\left(x-3\right)\left(x+4\right)\left(x^{2}-1\right)\right)^{2}}$$