Solve for a
a=\frac{5b}{b-2}
b\neq 2
Solve for b
b=\frac{2a}{a-5}
a\neq 5
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ab-2a=5b
Subtract 2a from both sides.
\left(b-2\right)a=5b
Combine all terms containing a.
\frac{\left(b-2\right)a}{b-2}=\frac{5b}{b-2}
Divide both sides by b-2.
a=\frac{5b}{b-2}
Dividing by b-2 undoes the multiplication by b-2.
ab-5b=2a
Subtract 5b from both sides.
\left(a-5\right)b=2a
Combine all terms containing b.
\frac{\left(a-5\right)b}{a-5}=\frac{2a}{a-5}
Divide both sides by a-5.
b=\frac{2a}{a-5}
Dividing by a-5 undoes the multiplication by a-5.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}