2x^2+9x+2x^2+16/(2x^2+9x+16x+72)x-2x^2+16x+7x+72/1= eching

$$\frac { 2 x ^ { 2 } + 9 x + 2 x ^ { 2 } + 16 } { ( 2 x ^ { 2 } + 9 x + 16 x + 72 ) x } - \frac { 2 x ^ { 2 } + 16 x + 7 x + 72 } { 1 } =$$

Baholash

$$\frac{16-5175x-3452x^{2}-863x^{3}-96x^{4}-4x^{5}}{x\left(x+8\right)\left(2x+9\right)}$$

Qisqa yechim qadamlari

4x^{2} ni olish uchun 2x^{2} va 2x^{2} ni birlashtirish.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+9x+16x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

25x ni olish uchun 9x va 16x ni birlashtirish.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

23x ni olish uchun 16x va 7x ni birlashtirish.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+23x+72}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\left(2x^{2}+23x+72\right)$$

2x^{2}+23x+72 teskarisini topish uchun har birining teskarisini toping.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-2x^{2}-23x-72$$

Faktor: \left(2x^{2}+25x+72\right)x.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-23x-72$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -2x^{2}-23x-72 ni \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)} marotabaga ko'paytirish.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} va \frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}$$

4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x kabi iboralarga o‘xshab birlashtiring.

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{x\left(x+8\right)\left(2x+9\right)}$$

x\left(x+8\right)\left(2x+9\right) ni kengaytirish.

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{2x^{3}+25x^{2}+72x}$$

Kengaytirish

$$\frac{16-5175x-3452x^{2}-863x^{3}-96x^{4}-4x^{5}}{x\left(2x^{2}+25x+72\right)}$$

Qisqa yechim qadamlari

4x^{2} ni olish uchun 2x^{2} va 2x^{2} ni birlashtirish.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+9x+16x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

25x ni olish uchun 9x va 16x ni birlashtirish.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

23x ni olish uchun 16x va 7x ni birlashtirish.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+23x+72}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\left(2x^{2}+23x+72\right)$$

2x^{2}+23x+72 teskarisini topish uchun har birining teskarisini toping.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-2x^{2}-23x-72$$

Faktor: \left(2x^{2}+25x+72\right)x.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-23x-72$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -2x^{2}-23x-72 ni \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)} marotabaga ko'paytirish.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} va \frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}$$

4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x kabi iboralarga o‘xshab birlashtiring.

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{x\left(x+8\right)\left(2x+9\right)}$$

x\left(x+8\right)\left(2x+9\right) ni kengaytirish.

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{2x^{3}+25x^{2}+72x}$$