Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{cx+1}{b}\text{, }&b\neq 0\text{ and }x\neq 0\\a\in \mathrm{C}\text{, }&c=-\frac{1}{x}\text{ and }x\neq 0\text{ and }b=0\end{matrix}\right.
Solve for b (complex solution)
\left\{\begin{matrix}b=\frac{cx+1}{a}\text{, }&a\neq 0\text{ and }x\neq 0\\b\in \mathrm{C}\text{, }&c=-\frac{1}{x}\text{ and }x\neq 0\text{ and }a=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{cx+1}{b}\text{, }&b\neq 0\text{ and }x\neq 0\\a\in \mathrm{R}\text{, }&c=-\frac{1}{x}\text{ and }x\neq 0\text{ and }b=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=\frac{cx+1}{a}\text{, }&a\neq 0\text{ and }x\neq 0\\b\in \mathrm{R}\text{, }&c=-\frac{1}{x}\text{ and }x\neq 0\text{ and }a=0\end{matrix}\right.
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-xc-1=-ab
Multiply both sides of the equation by x.
-ab=-xc-1
Swap sides so that all variable terms are on the left hand side.
-ab=-cx-1
Reorder the terms.
\left(-b\right)a=-cx-1
The equation is in standard form.
\frac{\left(-b\right)a}{-b}=\frac{-cx-1}{-b}
Divide both sides by -b.
a=\frac{-cx-1}{-b}
Dividing by -b undoes the multiplication by -b.
a=\frac{cx+1}{b}
Divide -1-xc by -b.
-xc-1=-ab
Multiply both sides of the equation by x.
-ab=-xc-1
Swap sides so that all variable terms are on the left hand side.
-ab=-cx-1
Reorder the terms.
\left(-a\right)b=-cx-1
The equation is in standard form.
\frac{\left(-a\right)b}{-a}=\frac{-cx-1}{-a}
Divide both sides by -a.
b=\frac{-cx-1}{-a}
Dividing by -a undoes the multiplication by -a.
b=\frac{cx+1}{a}
Divide -1-xc by -a.
-xc-1=-ab
Multiply both sides of the equation by x.
-ab=-xc-1
Swap sides so that all variable terms are on the left hand side.
-ab=-cx-1
Reorder the terms.
\left(-b\right)a=-cx-1
The equation is in standard form.
\frac{\left(-b\right)a}{-b}=\frac{-cx-1}{-b}
Divide both sides by -b.
a=\frac{-cx-1}{-b}
Dividing by -b undoes the multiplication by -b.
a=\frac{cx+1}{b}
Divide -1-xc by -b.
-xc-1=-ab
Multiply both sides of the equation by x.
-ab=-xc-1
Swap sides so that all variable terms are on the left hand side.
-ab=-cx-1
Reorder the terms.
\left(-a\right)b=-cx-1
The equation is in standard form.
\frac{\left(-a\right)b}{-a}=\frac{-cx-1}{-a}
Divide both sides by -a.
b=\frac{-cx-1}{-a}
Dividing by -a undoes the multiplication by -a.
b=\frac{cx+1}{a}
Divide -1-xc by -a.
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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.
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}