Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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\frac{5}{12}x+\frac{1}{5}+3=\frac{5}{12}x+\frac{16}{5}
Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.
\frac{5}{12}x+\frac{1}{5}+\frac{15}{5}=\frac{5}{12}x+\frac{16}{5}
Convert 3 to fraction \frac{15}{5}.
\frac{5}{12}x+\frac{1+15}{5}=\frac{5}{12}x+\frac{16}{5}
Since \frac{1}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.
\frac{5}{12}x+\frac{16}{5}=\frac{5}{12}x+\frac{16}{5}
Add 1 and 15 to get 16.
\frac{5}{12}x+\frac{16}{5}-\frac{5}{12}x=\frac{16}{5}
Subtract \frac{5}{12}x from both sides.
\frac{16}{5}=\frac{16}{5}
Combine \frac{5}{12}x and -\frac{5}{12}x to get 0.
\text{true}
Compare \frac{16}{5} and \frac{16}{5}.
x\in \mathrm{C}
This is true for any x.
\frac{5}{12}x+\frac{1}{5}+3=\frac{5}{12}x+\frac{16}{5}
Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.
\frac{5}{12}x+\frac{1}{5}+\frac{15}{5}=\frac{5}{12}x+\frac{16}{5}
Convert 3 to fraction \frac{15}{5}.
\frac{5}{12}x+\frac{1+15}{5}=\frac{5}{12}x+\frac{16}{5}
Since \frac{1}{5} and \frac{15}{5} have the same denominator, add them by adding their numerators.
\frac{5}{12}x+\frac{16}{5}=\frac{5}{12}x+\frac{16}{5}
Add 1 and 15 to get 16.
\frac{5}{12}x+\frac{16}{5}-\frac{5}{12}x=\frac{16}{5}
Subtract \frac{5}{12}x from both sides.
\frac{16}{5}=\frac{16}{5}
Combine \frac{5}{12}x and -\frac{5}{12}x to get 0.
\text{true}
Compare \frac{16}{5} and \frac{16}{5}.
x\in \mathrm{R}
This is true for any x.
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}