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\left(2x+1\right)\times 2=\left(x-1\right)\times 3
Variable x cannot be equal to any of the values -\frac{1}{2},1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(2x+1\right), the least common multiple of x-1,2x+1.
4x+2=\left(x-1\right)\times 3
Use the distributive property to multiply 2x+1 by 2.
4x+2=3x-3
Use the distributive property to multiply x-1 by 3.
4x+2-3x=-3
Subtract 3x from both sides.
x+2=-3
Combine 4x and -3x to get x.
x=-3-2
Subtract 2 from both sides.
x=-5
Subtract 2 from -3 to get -5.