(x+8/x^2-4-2/x-2)divx-4/x^2-4x+4 eching

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

Baholash

$$-\frac{x-2}{x+2}$$

Qisqa yechim qadamlari

Faktor: x^{2}-4.

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

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

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

\frac{x+8}{\left(x-2\right)\left(x+2\right)} va \frac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x+8-2\left(x+2\right) ichidagi ko‘paytirishlarni bajaring.

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

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

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

\frac{-x+4}{\left(x-2\right)\left(x+2\right)} ni \frac{x-4}{x^{2}-4x+4} ga bo'lish \frac{-x+4}{\left(x-2\right)\left(x+2\right)} ga k'paytirish \frac{x-4}{x^{2}-4x+4} ga qaytarish.

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

-x+4 mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala x-4 ni qisqartiring.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-2 ni qisqartiring.

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

Ifodani kengaytiring.

$$\frac{-x+2}{x+2}$$

Kengaytirish

$$-\frac{x-2}{x+2}$$

Qisqa yechim qadamlari

Faktor: x^{2}-4.

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

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

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

\frac{x+8}{\left(x-2\right)\left(x+2\right)} va \frac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

x+8-2\left(x+2\right) ichidagi ko‘paytirishlarni bajaring.

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

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

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

\frac{-x+4}{\left(x-2\right)\left(x+2\right)} ni \frac{x-4}{x^{2}-4x+4} ga bo'lish \frac{-x+4}{\left(x-2\right)\left(x+2\right)} ga k'paytirish \frac{x-4}{x^{2}-4x+4} ga qaytarish.

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

-x+4 mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala x-4 ni qisqartiring.

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

Hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-2 ni qisqartiring.

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

Ifodani kengaytiring.

$$\frac{-x+2}{x+2}$$