Solve for A
A=\frac{B}{B-2}
B\neq 2
Solve for B
B=\frac{2A}{A-1}
A\neq 1
Share
Copied to clipboard
AB-2A=B
Subtract 2A from both sides.
\left(B-2\right)A=B
Combine all terms containing A.
\frac{\left(B-2\right)A}{B-2}=\frac{B}{B-2}
Divide both sides by B-2.
A=\frac{B}{B-2}
Dividing by B-2 undoes the multiplication by B-2.
AB-B=2A
Subtract B from both sides.
\left(A-1\right)B=2A
Combine all terms containing B.
\frac{\left(A-1\right)B}{A-1}=\frac{2A}{A-1}
Divide both sides by A-1.
B=\frac{2A}{A-1}
Dividing by A-1 undoes the multiplication by A-1.
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}