Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{1+b-x}{2x+1}\text{, }&x\neq -\frac{1}{2}\\a\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }b=-\frac{3}{2}\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{1+b-x}{2x+1}\text{, }&x\neq -\frac{1}{2}\\a\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }b=-\frac{3}{2}\end{matrix}\right.
Solve for b
b=-2ax+x-a-1
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2ax+a=x-1-b
Subtract b from both sides.
\left(2x+1\right)a=x-1-b
Combine all terms containing a.
\left(2x+1\right)a=x-b-1
The equation is in standard form.
\frac{\left(2x+1\right)a}{2x+1}=\frac{x-b-1}{2x+1}
Divide both sides by 2x+1.
a=\frac{x-b-1}{2x+1}
Dividing by 2x+1 undoes the multiplication by 2x+1.
2ax+a=x-1-b
Subtract b from both sides.
\left(2x+1\right)a=x-1-b
Combine all terms containing a.
\left(2x+1\right)a=x-b-1
The equation is in standard form.
\frac{\left(2x+1\right)a}{2x+1}=\frac{x-b-1}{2x+1}
Divide both sides by 2x+1.
a=\frac{x-b-1}{2x+1}
Dividing by 2x+1 undoes the multiplication by 2x+1.
a+b=x-1-2ax
Subtract 2ax from both sides.
b=x-1-2ax-a
Subtract a from both sides.
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