Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{x+b}{x+1}\text{, }&x\neq -1\\a\in \mathrm{C}\text{, }&x=-1\text{ and }b=1\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{x+b}{x+1}\text{, }&x\neq -1\\a\in \mathrm{R}\text{, }&x=-1\text{ and }b=1\end{matrix}\right.
Solve for b
b=x\left(a-1\right)+a
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ax-x=b-a
Use the distributive property to multiply a-1 by x.
ax-x+a=b
Add a to both sides.
ax+a=b+x
Add x to both sides.
\left(x+1\right)a=b+x
Combine all terms containing a.
\left(x+1\right)a=x+b
The equation is in standard form.
\frac{\left(x+1\right)a}{x+1}=\frac{x+b}{x+1}
Divide both sides by x+1.
a=\frac{x+b}{x+1}
Dividing by x+1 undoes the multiplication by x+1.
ax-x=b-a
Use the distributive property to multiply a-1 by x.
ax-x+a=b
Add a to both sides.
ax+a=b+x
Add x to both sides.
\left(x+1\right)a=b+x
Combine all terms containing a.
\left(x+1\right)a=x+b
The equation is in standard form.
\frac{\left(x+1\right)a}{x+1}=\frac{x+b}{x+1}
Divide both sides by x+1.
a=\frac{x+b}{x+1}
Dividing by x+1 undoes the multiplication by x+1.
ax-x=b-a
Use the distributive property to multiply a-1 by x.
b-a=ax-x
Swap sides so that all variable terms are on the left hand side.
b=ax-x+a
Add a to both sides.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}