1/x(x+2)(x-2)-2/x(x^2+4) eching

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

Baholash

$$\frac{12-x^{2}}{x\left(x^{4}-16\right)}$$

Qisqa yechim qadamlari

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

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

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

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

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

$$\frac{x^{2}+4-2x^{2}-4x+4x+8}{x\left(x-2\right)\left(x+2\right)\left(x^{2}+4\right)}$$

x^{2}+4-2x^{2}-4x+4x+8 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-x^{2}+12}{x\left(x-2\right)\left(x+2\right)\left(x^{2}+4\right)}$$

x\left(x-2\right)\left(x+2\right)\left(x^{2}+4\right) ni kengaytirish.

$$\frac{-x^{2}+12}{x^{5}-16x}$$

Kengaytirish

$$\frac{12-x^{2}}{x\left(x^{4}-16\right)}$$

Qisqa yechim qadamlari

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

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

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

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

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

$$\frac{x^{2}+4-2x^{2}-4x+4x+8}{x\left(x-2\right)\left(x+2\right)\left(x^{2}+4\right)}$$

x^{2}+4-2x^{2}-4x+4x+8 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-x^{2}+12}{x\left(x-2\right)\left(x+2\right)\left(x^{2}+4\right)}$$

x\left(x-2\right)\left(x+2\right)\left(x^{2}+4\right) ni kengaytirish.

$$\frac{-x^{2}+12}{x^{5}-16x}$$