Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{a-1}{u-x}\text{, }&u\neq x\text{ and }a\neq 0\\b\in \mathrm{C}\text{, }&u=x\text{ and }a=1\end{matrix}\right.
Solve for a
a=bx-bu+1
u=x\text{ or }b\neq \frac{1}{u-x}
Solve for b
\left\{\begin{matrix}b=-\frac{a-1}{u-x}\text{, }&u\neq x\text{ and }a\neq 0\\b\in \mathrm{R}\text{, }&u=x\text{ and }a=1\end{matrix}\right.
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bu-2=bx-1+a\left(-1\right)
Multiply both sides of the equation by a.
bu-2-bx=-1+a\left(-1\right)
Subtract bx from both sides.
bu-bx=-1+a\left(-1\right)+2
Add 2 to both sides.
bu-bx=1+a\left(-1\right)
Add -1 and 2 to get 1.
\left(u-x\right)b=1+a\left(-1\right)
Combine all terms containing b.
\left(u-x\right)b=1-a
The equation is in standard form.
\frac{\left(u-x\right)b}{u-x}=\frac{1-a}{u-x}
Divide both sides by u-x.
b=\frac{1-a}{u-x}
Dividing by u-x undoes the multiplication by u-x.
bu-2=bx-1+a\left(-1\right)
Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.
bx-1+a\left(-1\right)=bu-2
Swap sides so that all variable terms are on the left hand side.
-1+a\left(-1\right)=bu-2-bx
Subtract bx from both sides.
a\left(-1\right)=bu-2-bx+1
Add 1 to both sides.
a\left(-1\right)=bu-1-bx
Add -2 and 1 to get -1.
-a=-bx+bu-1
The equation is in standard form.
\frac{-a}{-1}=\frac{-bx+bu-1}{-1}
Divide both sides by -1.
a=\frac{-bx+bu-1}{-1}
Dividing by -1 undoes the multiplication by -1.
a=bx-bu+1
Divide bu-1-bx by -1.
a=bx-bu+1\text{, }a\neq 0
Variable a cannot be equal to 0.
bu-2=bx-1+a\left(-1\right)
Multiply both sides of the equation by a.
bu-2-bx=-1+a\left(-1\right)
Subtract bx from both sides.
bu-bx=-1+a\left(-1\right)+2
Add 2 to both sides.
bu-bx=1+a\left(-1\right)
Add -1 and 2 to get 1.
\left(u-x\right)b=1+a\left(-1\right)
Combine all terms containing b.
\left(u-x\right)b=1-a
The equation is in standard form.
\frac{\left(u-x\right)b}{u-x}=\frac{1-a}{u-x}
Divide both sides by u-x.
b=\frac{1-a}{u-x}
Dividing by u-x undoes the multiplication by u-x.
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