2y-6/y^2-9-y/y-1+y^2+2/y^2+2y-3 eching

$$\frac { 2 y - 6 } { y ^ { 2 } - 9 } - \frac { y } { y - 1 } + \frac { y ^ { 2 } + 2 } { y ^ { 2 } + 2 y - 3 }$$

Baholash

$$-\frac{y}{\left(y-1\right)\left(y+3\right)}$$

Qisqa yechim qadamlari

\frac{2y-6}{y^{2}-9} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala y-3 ni qisqartiring.

$$\frac{2}{y+3}-\frac{y}{y-1}+\frac{y^{2}+2}{y^{2}+2y-3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. y+3 va y-1 ning eng kichik umumiy karralisi \left(y-1\right)\left(y+3\right). \frac{2}{y+3} ni \frac{y-1}{y-1} marotabaga ko'paytirish. \frac{y}{y-1} ni \frac{y+3}{y+3} marotabaga ko'paytirish.

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

\frac{2\left(y-1\right)}{\left(y-1\right)\left(y+3\right)} va \frac{y\left(y+3\right)}{\left(y-1\right)\left(y+3\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

2\left(y-1\right)-y\left(y+3\right) ichidagi ko‘paytirishlarni bajaring.

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

2y-2-y^{2}-3y kabi iboralarga o‘xshab birlashtiring.

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

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

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

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

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

-y-2-y^{2}+y^{2}+2 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-y}{\left(y-1\right)\left(y+3\right)}$$

\left(y-1\right)\left(y+3\right) ni kengaytirish.

$$\frac{-y}{y^{2}+2y-3}$$

Kengaytirish

$$-\frac{y}{\left(y-1\right)\left(y+3\right)}$$

Qisqa yechim qadamlari

\frac{2y-6}{y^{2}-9} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala y-3 ni qisqartiring.

$$\frac{2}{y+3}-\frac{y}{y-1}+\frac{y^{2}+2}{y^{2}+2y-3}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. y+3 va y-1 ning eng kichik umumiy karralisi \left(y-1\right)\left(y+3\right). \frac{2}{y+3} ni \frac{y-1}{y-1} marotabaga ko'paytirish. \frac{y}{y-1} ni \frac{y+3}{y+3} marotabaga ko'paytirish.

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

\frac{2\left(y-1\right)}{\left(y-1\right)\left(y+3\right)} va \frac{y\left(y+3\right)}{\left(y-1\right)\left(y+3\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

2\left(y-1\right)-y\left(y+3\right) ichidagi ko‘paytirishlarni bajaring.

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

2y-2-y^{2}-3y kabi iboralarga o‘xshab birlashtiring.

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

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

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

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

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

-y-2-y^{2}+y^{2}+2 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-y}{\left(y-1\right)\left(y+3\right)}$$

\left(y-1\right)\left(y+3\right) ni kengaytirish.

$$\frac{-y}{y^{2}+2y-3}$$