(x-2/x+1+5-x/x-2):[(1/x^2-x-2-1/x^2+3x+2)*(frac{x+1}{x}+frac{3-x^2}{x^2+x})] eching

$$( \frac { x - 2 } { x + 1 } + \frac { 5 - x } { x - 2 } ) : [ ( \frac { 1 } { x ^ { 2 } - x - 2 } - \frac { 1 } { x ^ { 2 } + 3 x + 2 } ) \cdot ( \frac { x + 1 } { x } + \frac { 3 - x ^ { 2 } } { x ^ { 2 } + x } ) ]$$

Baholash

$$\frac{9x\left(x+1\right)}{8}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+1 va x-2 ning eng kichik umumiy karralisi \left(x-2\right)\left(x+1\right). \frac{x-2}{x+1} ni \frac{x-2}{x-2} marotabaga ko'paytirish. \frac{5-x}{x-2} ni \frac{x+1}{x+1} marotabaga ko'paytirish.

$$\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} va \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

x^{2}-2x-2x+4+5x+5-x^{2}-x kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Faktor: x^{2}-x-2. Faktor: x^{2}+3x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Faktor: x^{2}+x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} va \frac{3-x^{2}}{x\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}$$

\left(x+1\right)\left(x+1\right)+3-x^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}$$

x^{2}+x+1+x+3-x^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} ni \frac{2x+4}{x\left(x+1\right)} ga ko‘paytiring.

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

\frac{9}{\left(x-2\right)\left(x+1\right)} ni \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} ga bo'lish \frac{9}{\left(x-2\right)\left(x+1\right)} ga k'paytirish \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} ga qaytarish.

$$\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}$$

Surat va maxrajdagi ikkala \left(x-2\right)\left(x+1\right) ni qisqartiring.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}$$

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}$$

Surat va maxrajdagi ikkala x+2 ni qisqartiring.

$$\frac{9x\left(x+1\right)}{2\times 4}$$

Ifodani kengaytiring.

$$\frac{9x^{2}+9x}{8}$$

Kengaytirish

$$\frac{9x^{2}+9x}{8}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+1 va x-2 ning eng kichik umumiy karralisi \left(x-2\right)\left(x+1\right). \frac{x-2}{x+1} ni \frac{x-2}{x-2} marotabaga ko'paytirish. \frac{5-x}{x-2} ni \frac{x+1}{x+1} marotabaga ko'paytirish.

$$\frac{\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}+\frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

\frac{\left(x-2\right)\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} va \frac{\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

\left(x-2\right)\left(x-2\right)+\left(5-x\right)\left(x+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{x^{2}-2x-2x+4+5x+5-x^{2}-x}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

x^{2}-2x-2x+4+5x+5-x^{2}-x kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{x^{2}-x-2}-\frac{1}{x^{2}+3x+2}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Faktor: x^{2}-x-2. Faktor: x^{2}+3x+2.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{1}{\left(x-2\right)\left(x+1\right)}-\frac{1}{\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\left(\frac{x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\right)\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{x+2-x+2}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x^{2}+x}\right)}$$

Faktor: x^{2}+x.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{x+1}{x}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

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

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\left(\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)}+\frac{3-x^{2}}{x\left(x+1\right)}\right)}$$

\frac{\left(x+1\right)\left(x+1\right)}{x\left(x+1\right)} va \frac{3-x^{2}}{x\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{\left(x+1\right)\left(x+1\right)+3-x^{2}}{x\left(x+1\right)}}$$

\left(x+1\right)\left(x+1\right)+3-x^{2} ichidagi ko‘paytirishlarni bajaring.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{x^{2}+x+1+x+3-x^{2}}{x\left(x+1\right)}}$$

x^{2}+x+1+x+3-x^{2} kabi iboralarga o‘xshab birlashtiring.

$$\frac{\frac{9}{\left(x-2\right)\left(x+1\right)}}{\frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)}\times \frac{2x+4}{x\left(x+1\right)}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{\left(x-2\right)\left(x+1\right)\left(x+2\right)} ni \frac{2x+4}{x\left(x+1\right)} ga ko‘paytiring.

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

\frac{9}{\left(x-2\right)\left(x+1\right)} ni \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} ga bo'lish \frac{9}{\left(x-2\right)\left(x+1\right)} ga k'paytirish \frac{4\left(2x+4\right)}{\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)} ga qaytarish.

$$\frac{9\left(x-2\right)\left(x+1\right)\left(x+2\right)x\left(x+1\right)}{\left(x-2\right)\left(x+1\right)\times 4\left(2x+4\right)}$$

Surat va maxrajdagi ikkala \left(x-2\right)\left(x+1\right) ni qisqartiring.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{4\left(2x+4\right)}$$

Hali faktorlanmagan ifodalarni faktorlang.

$$\frac{9x\left(x+1\right)\left(x+2\right)}{2\times 4\left(x+2\right)}$$

Surat va maxrajdagi ikkala x+2 ni qisqartiring.

$$\frac{9x\left(x+1\right)}{2\times 4}$$

Ifodani kengaytiring.

$$\frac{9x^{2}+9x}{8}$$