3beta/alpha+1+3alpha/beta+1 eching

$$\frac { 3 \beta } { \alpha + 1 } + \frac { 3 \alpha } { \beta + 1 }$$

Baholash

$$\frac{3\left(\alpha ^{2}+\alpha +\beta ^{2}+\beta \right)}{\left(\alpha +1\right)\left(\beta +1\right)}$$

Qisqa yechim qadamlari

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

$$\frac{3\beta \left(\beta +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)}+\frac{3\alpha \left(\alpha +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)}$$

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

$$\frac{3\beta \left(\beta +1\right)+3\alpha \left(\alpha +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)}$$

3\beta \left(\beta +1\right)+3\alpha \left(\alpha +1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{3\beta ^{2}+3\beta +3\alpha ^{2}+3\alpha }{\left(\alpha +1\right)\left(\beta +1\right)}$$

\left(\alpha +1\right)\left(\beta +1\right) ni kengaytirish.

$$\frac{3\beta ^{2}+3\beta +3\alpha ^{2}+3\alpha }{\alpha \beta +\alpha +\beta +1}$$

Omil

$$\frac{3\left(\alpha ^{2}+\alpha +\beta ^{2}+\beta \right)}{\left(\alpha +1\right)\left(\beta +1\right)}$$