Solve for a
a=-\frac{4}{b}
b\neq 0
Solve for b
b=-\frac{4}{a}
a\neq 0
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1-5=ab
Multiply both sides of the equation by b.
-4=ab
Subtract 5 from 1 to get -4.
ab=-4
Swap sides so that all variable terms are on the left hand side.
ba=-4
The equation is in standard form.
\frac{ba}{b}=-\frac{4}{b}
Divide both sides by b.
a=-\frac{4}{b}
Dividing by b undoes the multiplication by b.
1-5=ab
Variable b cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by b.
-4=ab
Subtract 5 from 1 to get -4.
ab=-4
Swap sides so that all variable terms are on the left hand side.
\frac{ab}{a}=-\frac{4}{a}
Divide both sides by a.
b=-\frac{4}{a}
Dividing by a undoes the multiplication by a.
b=-\frac{4}{a}\text{, }b\neq 0
Variable b cannot be equal to 0.
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}