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

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

Baholash

$$4$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{xx}{x} va \frac{1}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

xx+1 ichidagi ko‘paytirishlarni bajaring.

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

\frac{x^{2}+1}{x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{x}{x} marotabaga ko'paytirish.

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

\frac{xx}{x} va \frac{1}{x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

xx-1 ichidagi ko‘paytirishlarni bajaring.

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

\frac{x^{2}-1}{x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

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

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

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

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

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

x^{4}+2x^{2}+1-x^{4}+2x^{2}-1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{4x^{2}}{x^{2}}$$

Surat va maxrajdagi ikkala x^{2} ni qisqartiring.

$$4$$

Omil

$$2^{2}$$