Solve for b
b=-1+\frac{e}{x}
x\neq 0
Solve for x
x=\frac{e}{b+1}
b\neq -1
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xb+x=e
Swap sides so that all variable terms are on the left hand side.
xb=e-x
Subtract x from both sides.
\frac{xb}{x}=\frac{e-x}{x}
Divide both sides by x.
b=\frac{e-x}{x}
Dividing by x undoes the multiplication by x.
b=-1+\frac{e}{x}
Divide e-x by x.
xb+x=e
Swap sides so that all variable terms are on the left hand side.
\left(b+1\right)x=e
Combine all terms containing x.
\frac{\left(b+1\right)x}{b+1}=\frac{e}{b+1}
Divide both sides by 1+b.
x=\frac{e}{b+1}
Dividing by 1+b undoes the multiplication by 1+b.
Examples
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{ 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}