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

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

Baholash

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

Qisqa yechim qadamlari

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

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

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

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

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

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

x-1+x+1 kabi iboralarga o‘xshab birlashtiring.

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

Surat va maxrajdagi ikkala x ni qisqartiring.

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

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

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

x ga nisbatan hosilani topish

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