Leysa alpha/beta+1+beta/alpha+1

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

Meta

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

Skref að einfaldri lausn

Til að leggja saman eða draga saman segðir skaltu stækka þær til að nefnararnir verði eins. Minnsta sameiginlega margfeldi \beta +1 og \alpha +1 er \left(\alpha +1\right)\left(\beta +1\right). Margfaldaðu \frac{\alpha }{\beta +1} sinnum \frac{\alpha +1}{\alpha +1}. Margfaldaðu \frac{\beta }{\alpha +1} sinnum \frac{\beta +1}{\beta +1}.

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

Þar sem \frac{\alpha \left(\alpha +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)} og \frac{\beta \left(\beta +1\right)}{\left(\alpha +1\right)\left(\beta +1\right)} eru með sama nefnara skaltu leggja saman með því að leggja saman teljarana.

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

Margfaldaðu í \alpha \left(\alpha +1\right)+\beta \left(\beta +1\right).

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

Víkka \left(\alpha +1\right)\left(\beta +1\right).

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

Diffra með hliðsjón af α

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