(x^{2}-1/2x)-[3x+1/2x^{3}-(1/2x^{2}+7x+x^3)+(-2x^3)^2:(2x)^3] eching

$$( x ^ { 2 } - \frac { 1 } { 2 } x ) - [ 3 x + \frac { 1 } { 2 } x ^ { 3 } - ( \frac { 1 } { 2 } x ^ { 2 } + 7 x + x ^ { 3 } ) + ( - 2 x ^ { 3 } ) ^ { 2 } : ( 2 x ) ^ { 3 } ]$$

Baholash

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

Yechim qadamlari

\frac{1}{2}x^{2}+7x+x^{3} teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-\frac{1}{2}x-\left(3x+\frac{1}{2}x^{3}-\frac{1}{2}x^{2}-7x-x^{3}+\frac{\left(-2x^{3}\right)^{2}}{\left(2x\right)^{3}}\right)$$

-4x ni olish uchun 3x va -7x ni birlashtirish.

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

-\frac{1}{2}x^{3} ni olish uchun \frac{1}{2}x^{3} va -x^{3} ni birlashtirish.

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

\left(-2x^{3}\right)^{2} ni kengaytirish.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 2 ni ko‘paytirib, 6 ni oling.

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

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

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

\left(2x\right)^{3} ni kengaytirish.

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

3 daraja ko‘rsatkichini 2 ga hisoblang va 8 ni qiymatni oling.

$$x^{2}-\frac{1}{2}x-\left(-4x-\frac{1}{2}x^{3}-\frac{1}{2}x^{2}+\frac{4x^{6}}{8x^{3}}\right)$$

Surat va maxrajdagi ikkala 4x^{3} ni qisqartiring.

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

0 ni olish uchun -\frac{1}{2}x^{3} va \frac{x^{3}}{2} ni birlashtirish.

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

-4x-\frac{1}{2}x^{2} teskarisini topish uchun har birining teskarisini toping.

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

\frac{7}{2}x ni olish uchun -\frac{1}{2}x va 4x ni birlashtirish.

$$x^{2}+\frac{7}{2}x+\frac{1}{2}x^{2}$$

\frac{3}{2}x^{2} ni olish uchun x^{2} va \frac{1}{2}x^{2} ni birlashtirish.

$$\frac{3}{2}x^{2}+\frac{7}{2}x$$

Kengaytirish

$$\frac{3x^{2}+7x}{2}$$

Yechim qadamlari

\frac{1}{2}x^{2}+7x+x^{3} teskarisini topish uchun har birining teskarisini toping.

$$x^{2}-\frac{1}{2}x-\left(3x+\frac{1}{2}x^{3}-\frac{1}{2}x^{2}-7x-x^{3}+\frac{\left(-2x^{3}\right)^{2}}{\left(2x\right)^{3}}\right)$$

-4x ni olish uchun 3x va -7x ni birlashtirish.

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

-\frac{1}{2}x^{3} ni olish uchun \frac{1}{2}x^{3} va -x^{3} ni birlashtirish.

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

\left(-2x^{3}\right)^{2} ni kengaytirish.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 2 ni ko‘paytirib, 6 ni oling.

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

2 daraja ko‘rsatkichini -2 ga hisoblang va 4 ni qiymatni oling.

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

\left(2x\right)^{3} ni kengaytirish.

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

3 daraja ko‘rsatkichini 2 ga hisoblang va 8 ni qiymatni oling.

$$x^{2}-\frac{1}{2}x-\left(-4x-\frac{1}{2}x^{3}-\frac{1}{2}x^{2}+\frac{4x^{6}}{8x^{3}}\right)$$

Surat va maxrajdagi ikkala 4x^{3} ni qisqartiring.

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

0 ni olish uchun -\frac{1}{2}x^{3} va \frac{x^{3}}{2} ni birlashtirish.

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

-4x-\frac{1}{2}x^{2} teskarisini topish uchun har birining teskarisini toping.

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

\frac{7}{2}x ni olish uchun -\frac{1}{2}x va 4x ni birlashtirish.

$$x^{2}+\frac{7}{2}x+\frac{1}{2}x^{2}$$

\frac{3}{2}x^{2} ni olish uchun x^{2} va \frac{1}{2}x^{2} ni birlashtirish.

$$\frac{3}{2}x^{2}+\frac{7}{2}x$$