Solve for a
a=-\frac{3b-2}{b-1}
b\neq 1
Solve for b
b=\frac{a+2}{a+3}
a\neq -3
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ab-a-2=-3b
Subtract 3b from both sides. Anything subtracted from zero gives its negation.
ab-a=-3b+2
Add 2 to both sides.
\left(b-1\right)a=-3b+2
Combine all terms containing a.
\left(b-1\right)a=2-3b
The equation is in standard form.
\frac{\left(b-1\right)a}{b-1}=\frac{2-3b}{b-1}
Divide both sides by b-1.
a=\frac{2-3b}{b-1}
Dividing by b-1 undoes the multiplication by b-1.
ab+3b-2=a
Add a to both sides. Anything plus zero gives itself.
ab+3b=a+2
Add 2 to both sides.
\left(a+3\right)b=a+2
Combine all terms containing b.
\frac{\left(a+3\right)b}{a+3}=\frac{a+2}{a+3}
Divide both sides by a+3.
b=\frac{a+2}{a+3}
Dividing by a+3 undoes the multiplication by a+3.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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