Lutasin ang 3beta/alpha+1+3alpha/beta+1

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

I-evaluate

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

Maiikling Hakbang sa Solution

Para magdagdag o mag-subtract ng mga expression, i-expand ang mga iyon para gawing magkakapareho ang mga denominator ng mga ito. Ang least common multiple ng \alpha +1 at \beta +1 ay \left(\alpha +1\right)\left(\beta +1\right). I-multiply ang \frac{3\beta }{\alpha +1} times \frac{\beta +1}{\beta +1}. I-multiply ang \frac{3\alpha }{\beta +1} times \frac{\alpha +1}{\alpha +1}.

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

Dahil may parehong denominator ang \frac{3\beta \left(\beta +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)} at \frac{3\alpha \left(\alpha +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)}, pagsamahin ang mga ito sa pamamagitan ng pagsasama sa mga numerator ng mga ito.

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

Gawin ang mga pag-multiply sa 3\beta \left(\beta +1\right)+3\alpha \left(\alpha +1\right).

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

Palawakin ang \left(\alpha +1\right)\left(\beta +1\right).

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

I-factor

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