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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