1/2x-7/14+12/16x^2 eching

$$\frac { 1 } { 2 x } - \frac { 7 } { 14 } + \frac { 12 } { 16 x ^ { 2 } }$$

Baholash

$$-\frac{1}{2}+\frac{1}{2x}+\frac{3}{4x^{2}}$$

Qisqa yechim qadamlari

\frac{7}{14} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2x}-\frac{1}{2}+\frac{12}{16x^{2}}$$

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

$$\frac{1}{2x}-\frac{x}{2x}+\frac{12}{16x^{2}}$$

\frac{1}{2x} va \frac{x}{2x} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{1-x}{2x}+\frac{12}{16x^{2}}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2x va 16x^{2} ning eng kichik umumiy karralisi 16x^{2}. \frac{1-x}{2x} ni \frac{8x}{8x} marotabaga ko'paytirish.

$$\frac{\left(1-x\right)\times 8x}{16x^{2}}+\frac{12}{16x^{2}}$$

\frac{\left(1-x\right)\times 8x}{16x^{2}} va \frac{12}{16x^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\left(1-x\right)\times 8x+12}{16x^{2}}$$

\left(1-x\right)\times 8x+12 ichidagi ko‘paytirishlarni bajaring.

$$\frac{8x-8x^{2}+12}{16x^{2}}$$

\frac{8x-8x^{2}+12}{16x^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala 2\times 4 ni qisqartiring.

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

Surat va maxrajdagi ikkala -1 ni qisqartiring.

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

-\frac{1}{2}\sqrt{7}+\frac{1}{2} teskarisini topish uchun har birining teskarisini toping.

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

\frac{1}{2}\sqrt{7}+\frac{1}{2} teskarisini topish uchun har birining teskarisini toping.

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

x+\frac{1}{2}\sqrt{7}-\frac{1}{2} ga x-\frac{1}{2}\sqrt{7}-\frac{1}{2} ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

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

\sqrt{7} kvadrati – 7.

$$\frac{x^{2}-x-\frac{1}{4}\times 7+\frac{1}{4}}{-2x^{2}}$$

-\frac{7}{4} hosil qilish uchun -\frac{1}{4} va 7 ni ko'paytirish.

$$\frac{x^{2}-x-\frac{7}{4}+\frac{1}{4}}{-2x^{2}}$$

-\frac{3}{2} olish uchun -\frac{7}{4} va \frac{1}{4}'ni qo'shing.

$$\frac{x^{2}-x-\frac{3}{2}}{-2x^{2}}$$

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala 2 ni qisqartiring.

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

Ifodani kengaytiring.

$$\frac{\frac{1}{2}x^{2}-\frac{1}{2}x-\frac{3}{4}}{-x^{2}}$$

Omil

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