Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{1}{x+3}\text{, }&x\neq -3\\a\in \mathrm{C}\text{, }&x=-1\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{1}{x+3}\text{, }&x\neq -3\\a\in \mathrm{R}\text{, }&x=-1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=-1\text{, }&\text{unconditionally}\\x=-3+\frac{1}{a}\text{, }&a\neq 0\end{matrix}\right.
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\left(x^{2}+4x+3\right)a=x+1
Combine all terms containing a.
\frac{\left(x^{2}+4x+3\right)a}{x^{2}+4x+3}=\frac{x+1}{x^{2}+4x+3}
Divide both sides by x^{2}+4x+3.
a=\frac{x+1}{x^{2}+4x+3}
Dividing by x^{2}+4x+3 undoes the multiplication by x^{2}+4x+3.
a=\frac{1}{x+3}
Divide 1+x by x^{2}+4x+3.
\left(x^{2}+4x+3\right)a=x+1
Combine all terms containing a.
\frac{\left(x^{2}+4x+3\right)a}{x^{2}+4x+3}=\frac{x+1}{x^{2}+4x+3}
Divide both sides by x^{2}+4x+3.
a=\frac{x+1}{x^{2}+4x+3}
Dividing by x^{2}+4x+3 undoes the multiplication by x^{2}+4x+3.
a=\frac{1}{x+3}
Divide 1+x by x^{2}+4x+3.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Matrix
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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}