4/(x-1)-5/(x+2)=3/x

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Solution for 4/(x-1)-5/(x+2)=3/x equation:



4/(x-1)-5/(x+2)=3/x
We move all terms to the left:
4/(x-1)-5/(x+2)-(3/x)=0
Domain of the equation: (x-1)!=0
We move all terms containing x to the left, all other terms to the right
x!=1
x∈R
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)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
4/(x-1)-5/(x+2)-(+3/x)=0
We get rid of parentheses
4/(x-1)-5/(x+2)-3/x=0
We calculate fractions
(-5x^2+5x)/((x-1)*(x+2)*x)+(4x^2+8x)/((x-1)*(x+2)*x)+(-3*(x-1)*(x+2))/((x-1)*(x+2)*x)=0
We calculate terms in parentheses: +(-5x^2+5x)/((x-1)*(x+2)*x), so:
-5x^2+5x)/((x-1)*(x+2)*x
We multiply all the terms by the denominator
-5x^2*((x-1)*(x+2)*x+5x)
Back to the equation:
+(-5x^2*((x-1)*(x+2)*x+5x))
We calculate terms in parentheses: +(4x^2+8x)/((x-1)*(x+2)*x), so:
4x^2+8x)/((x-1)*(x+2)*x
We multiply all the terms by the denominator
4x^2*((x-1)*(x+2)*x+8x)
Back to the equation:
+(4x^2*((x-1)*(x+2)*x+8x))
We calculate terms in parentheses: +(-3*(x-1)*(x+2))/((x-1)*(x+2)*x), so:
-3*(x-1)*(x+2))/((x-1)*(x+2)*x
We multiply all the terms by the denominator
-3*(x-1)*(x+2))
Back to the equation:
+(-3*(x-1)*(x+2)))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)
We calculate terms in parentheses: +(-3*(x-1)*(x+2))), so:
-3*(x-1)*(x+2))
We calculate terms in parentheses: +(-5x^2*((x-1)*(x+2)*x+5x)), so:
-5x^2*((x-1)*(x+2)*x+5x)
We calculate terms in parentheses: +(4x^2*((x-1)*(x+2)*x+8x)), so:
4x^2*((x-1)*(x+2)*x+8x)

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