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\left(x-1\right)\times 4-x=0
Variable x cannot be equal to any of the values 0,1 since division by zero is not defined. Multiply both sides of the equation by x\left(x-1\right), the least common multiple of x,x-1.
4x-4-x=0
Use the distributive property to multiply x-1 by 4.
4x-x=4
Add 4 to both sides. Anything plus zero gives itself.
3x=4
Combine 4x and -x to get 3x.
x=\frac{4}{3}
Divide both sides by 3.