Solve for α
\alpha =\frac{\beta +2}{\beta -1}
\beta \neq 1
Solve for β
\beta =\frac{\alpha +2}{\alpha -1}
\alpha \neq 1
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\alpha \beta -\alpha -\beta +1=3
Use the distributive property to multiply \alpha -1 by \beta -1.
\alpha \beta -\alpha +1=3+\beta
Add \beta to both sides.
\alpha \beta -\alpha =3+\beta -1
Subtract 1 from both sides.
\alpha \beta -\alpha =2+\beta
Subtract 1 from 3 to get 2.
\left(\beta -1\right)\alpha =2+\beta
Combine all terms containing \alpha .
\left(\beta -1\right)\alpha =\beta +2
The equation is in standard form.
\frac{\left(\beta -1\right)\alpha }{\beta -1}=\frac{\beta +2}{\beta -1}
Divide both sides by \beta -1.
\alpha =\frac{\beta +2}{\beta -1}
Dividing by \beta -1 undoes the multiplication by \beta -1.
\alpha \beta -\alpha -\beta +1=3
Use the distributive property to multiply \alpha -1 by \beta -1.
\alpha \beta -\beta +1=3+\alpha
Add \alpha to both sides.
\alpha \beta -\beta =3+\alpha -1
Subtract 1 from both sides.
\alpha \beta -\beta =2+\alpha
Subtract 1 from 3 to get 2.
\left(\alpha -1\right)\beta =2+\alpha
Combine all terms containing \beta .
\left(\alpha -1\right)\beta =\alpha +2
The equation is in standard form.
\frac{\left(\alpha -1\right)\beta }{\alpha -1}=\frac{\alpha +2}{\alpha -1}
Divide both sides by \alpha -1.
\beta =\frac{\alpha +2}{\alpha -1}
Dividing by \alpha -1 undoes the multiplication by \alpha -1.
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