2(x+4)/(x-2)+3=2x+1/x-2

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Solution for 2(x+4)/(x-2)+3=2x+1/x-2 equation:



2(x+4)/(x-2)+3=2x+1/x-2
We move all terms to the left:
2(x+4)/(x-2)+3-(2x+1/x-2)=0
Domain of the equation: (x-2)!=0
We move all terms containing x to the left, all other terms to the right
x!=2
x∈R
Domain of the equation: x-2)!=0
x∈R
We get rid of parentheses
2(x+4)/(x-2)-2x-1/x+2+3=0
We calculate fractions
-2x+(2x^2+8x)/(x^2-2x)+(-1*(x-2))/(x^2-2x)+2+3=0
We calculate terms in parentheses: +(-1*(x-2))/(x^2-2x), so:
-1*(x-2))/(x^2-2x
We add all the numbers together, and all the variables
-2x-1*(x-2))/(x^2
We multiply all the terms by the denominator
-2x*(x^2-1*(x-2))
Back to the equation:
+(-2x*(x^2-1*(x-2)))
We add all the numbers together, and all the variables
-2x+(2x^2+8x)/(x^2-2x)+(-2x*(x^2-1*(x-2)))+5=0
We multiply all the terms by the denominator
-2x*(x^2-2x)+(2x^2+8x)+((-2x*(x^2-1*(x-2))))*(x^2-2x)+5*(x^2-2x)=0
We calculate terms in parentheses: +((-2x*(x^2-1*(x-2))))*(x^2-2x), so:
(-2x*(x^2-1*(x-2))))*(x^2-2x
We add all the numbers together, and all the variables
-2x+(-2x*(x^2-1*(x-2))))*(x^2
Back to the equation:
+(-2x+(-2x*(x^2-1*(x-2))))*(x^2)
We multiply parentheses
-2x^3+4x^2+5x^2+(2x^2+8x)+(-2x+(-2x*(x^2-1*(x-2))))*x^2-10x=0
We get rid of parentheses
-2x^3+4x^2+5x^2+2x^2+8x+(-2x+(-2x*(x^2-1*(x-2))))*x^2-10x=0
We do not support expression: x^3

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