Solve for n (complex solution)
\left\{\begin{matrix}n=-\frac{1}{\Delta -1}\text{, }&\Delta \neq 1\\n\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&\Delta =\frac{n-1}{n}\text{ and }n\neq 0\end{matrix}\right.
Solve for n
\left\{\begin{matrix}n=-\frac{1}{\Delta -1}\text{, }&\Delta \neq 1\\n\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&\Delta =\frac{n-1}{n}\text{ and }n\neq 0\end{matrix}\right.
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\Delta xn=xn-x
Use the distributive property to multiply x by n-1.
\Delta xn-xn=-x
Subtract xn from both sides.
\left(\Delta x-x\right)n=-x
Combine all terms containing n.
\left(x\Delta -x\right)n=-x
The equation is in standard form.
\frac{\left(x\Delta -x\right)n}{x\Delta -x}=-\frac{x}{x\Delta -x}
Divide both sides by \Delta x-x.
n=-\frac{x}{x\Delta -x}
Dividing by \Delta x-x undoes the multiplication by \Delta x-x.
n=-\frac{1}{\Delta -1}
Divide -x by \Delta x-x.
\Delta xn=xn-x
Use the distributive property to multiply x by n-1.
\Delta xn-xn=-x
Subtract xn from both sides.
\Delta xn-xn+x=0
Add x to both sides.
\left(\Delta n-n+1\right)x=0
Combine all terms containing x.
\left(n\Delta -n+1\right)x=0
The equation is in standard form.
x=0
Divide 0 by n\Delta -n+1.
\Delta xn=xn-x
Use the distributive property to multiply x by n-1.
\Delta xn-xn=-x
Subtract xn from both sides.
\left(\Delta x-x\right)n=-x
Combine all terms containing n.
\left(x\Delta -x\right)n=-x
The equation is in standard form.
\frac{\left(x\Delta -x\right)n}{x\Delta -x}=-\frac{x}{x\Delta -x}
Divide both sides by \Delta x-x.
n=-\frac{x}{x\Delta -x}
Dividing by \Delta x-x undoes the multiplication by \Delta x-x.
n=-\frac{1}{\Delta -1}
Divide -x by \Delta x-x.
\Delta xn=xn-x
Use the distributive property to multiply x by n-1.
\Delta xn-xn=-x
Subtract xn from both sides.
\Delta xn-xn+x=0
Add x to both sides.
\left(\Delta n-n+1\right)x=0
Combine all terms containing x.
\left(n\Delta -n+1\right)x=0
The equation is in standard form.
x=0
Divide 0 by n\Delta -n+1.
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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}