Solve for x
x=\frac{1}{5}=0.2
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\left(x-2\right)\left(x-3\right)=\left(x+1\right)\left(x+4\right)
Variable x cannot be equal to any of the values -1,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+1\right), the least common multiple of x+1,x-2.
x^{2}-5x+6=\left(x+1\right)\left(x+4\right)
Use the distributive property to multiply x-2 by x-3 and combine like terms.
x^{2}-5x+6=x^{2}+5x+4
Use the distributive property to multiply x+1 by x+4 and combine like terms.
x^{2}-5x+6-x^{2}=5x+4
Subtract x^{2} from both sides.
-5x+6=5x+4
Combine x^{2} and -x^{2} to get 0.
-5x+6-5x=4
Subtract 5x from both sides.
-10x+6=4
Combine -5x and -5x to get -10x.
-10x=4-6
Subtract 6 from both sides.
-10x=-2
Subtract 6 from 4 to get -2.
x=\frac{-2}{-10}
Divide both sides by -10.
x=\frac{1}{5}
Reduce the fraction \frac{-2}{-10} to lowest terms by extracting and canceling out -2.
Examples
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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
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