Solve for x
x = \frac{9}{5} = 1\frac{4}{5} = 1.8
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\left(x-1\right)\times 3-\left(3-x\right)\times 2=0
Variable x cannot be equal to any of the values 1,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x-1\right), the least common multiple of x-3,1-x.
3x-3-\left(3-x\right)\times 2=0
Use the distributive property to multiply x-1 by 3.
3x-3-\left(6-2x\right)=0
Use the distributive property to multiply 3-x by 2.
3x-3-6+2x=0
To find the opposite of 6-2x, find the opposite of each term.
3x-9+2x=0
Subtract 6 from -3 to get -9.
5x-9=0
Combine 3x and 2x to get 5x.
5x=9
Add 9 to both sides. Anything plus zero gives itself.
x=\frac{9}{5}
Divide both sides by 5.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}