2x/x-3+1/2x+3+3x+9/(x-3)(2x+3) eching

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

Baholash

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

Qisqa yechim qadamlari

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

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

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

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

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

$$\frac{4x^{2}+6x+x-3}{\left(x-3\right)\left(2x+3\right)}+\frac{3x+9}{\left(x-3\right)\left(2x+3\right)}$$

4x^{2}+6x+x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{4x^{2}+7x-3}{\left(x-3\right)\left(2x+3\right)}+\frac{3x+9}{\left(x-3\right)\left(2x+3\right)}$$

\frac{4x^{2}+7x-3}{\left(x-3\right)\left(2x+3\right)} va \frac{3x+9}{\left(x-3\right)\left(2x+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{4x^{2}+7x-3+3x+9}{\left(x-3\right)\left(2x+3\right)}$$

4x^{2}+7x-3+3x+9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{4x^{2}+10x+6}{\left(x-3\right)\left(2x+3\right)}$$

\frac{4x^{2}+10x+6}{\left(x-3\right)\left(2x+3\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala 2x+3 ni qisqartiring.

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

2 ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

Kengaytirish

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

Qisqa yechim qadamlari

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

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

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

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

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

$$\frac{4x^{2}+6x+x-3}{\left(x-3\right)\left(2x+3\right)}+\frac{3x+9}{\left(x-3\right)\left(2x+3\right)}$$

4x^{2}+6x+x-3 kabi iboralarga o‘xshab birlashtiring.

$$\frac{4x^{2}+7x-3}{\left(x-3\right)\left(2x+3\right)}+\frac{3x+9}{\left(x-3\right)\left(2x+3\right)}$$

\frac{4x^{2}+7x-3}{\left(x-3\right)\left(2x+3\right)} va \frac{3x+9}{\left(x-3\right)\left(2x+3\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{4x^{2}+7x-3+3x+9}{\left(x-3\right)\left(2x+3\right)}$$

4x^{2}+7x-3+3x+9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{4x^{2}+10x+6}{\left(x-3\right)\left(2x+3\right)}$$

\frac{4x^{2}+10x+6}{\left(x-3\right)\left(2x+3\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala 2x+3 ni qisqartiring.

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

2 ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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