5x/(3x-3)+6/(x+2)=5/3

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Solution for 5x/(3x-3)+6/(x+2)=5/3 equation: 



5x/(3x-3)+6/(x+2)=5/3

We move all terms to the left:

5x/(3x-3)+6/(x+2)-(5/3)=0



Domain of the equation: (3x-3)!=0

We move all terms containing x to the left, all other terms to the right

3x!=3

x!=3/3

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



We add all the numbers together, and all the variables

5x/(3x-3)+6/(x+2)-(+5/3)=0

We get rid of parentheses

5x/(3x-3)+6/(x+2)-5/3=0

We calculate fractions


(15x^2+30x)/((3x-3)*(x+2)*3)+(54x-54)/((3x-3)*(x+2)*3)+(-5*(3x-3)*(x+2))/((3x-3)*(x+2)*3)=0



We calculate terms in parentheses: +(15x^2+30x)/((3x-3)*(x+2)*3), so:

15x^2+30x)/((3x-3)*(x+2)*3

We multiply all the terms by the denominator


15x^2*((3x-3)*(x+2)*3+30x)

Back to the equation:

+(15x^2*((3x-3)*(x+2)*3+30x))





We calculate terms in parentheses: +(54x-54)/((3x-3)*(x+2)*3), so:

54x-54)/((3x-3)*(x+2)*3

We multiply all the terms by the denominator


54x*((3x-3)*(x+2)*3-54)

Back to the equation:

+(54x*((3x-3)*(x+2)*3-54))





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))/((3x-3)*(x+2)*3), so:

-5*(3x-3)*(x+2))/((3x-3)*(x+2)*3

We multiply all the terms by the denominator


-5*(3x-3)*(x+2))

Back to the equation:

+(-5*(3x-3)*(x+2)))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





We calculate terms in parentheses: +(-5*(3x-3)*(x+2))), so:

-5*(3x-3)*(x+2))





We calculate terms in parentheses: +(15x^2*((3x-3)*(x+2)*3+30x)), so:

15x^2*((3x-3)*(x+2)*3+30x)





We calculate terms in parentheses: +(54x*((3x-3)*(x+2)*3-54)), so:

54x*((3x-3)*(x+2)*3-54)





							

									
									
									
									
									
									

														
			

			
				

						
				
				
					
			
						
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