6/(x-1)=-9/(x-6)

Solution for 6/(x-1)=-9/(x-6) equation:

6/(x-1)=-9/(x-6)

We move all terms to the left:

6/(x-1)-(-9/(x-6))=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-6))!=0

x∈R


We calculate fractions


6x/((x-1)*(x-6)))+(-(-9*(x-1))/((x-1)*(x-6)))=0


We calculate terms in parentheses: -(-9*(x-1))/((x-1)*(x-6))), so:

-9*(x-1))/((x-1)*(x-6))

We multiply all the terms by the denominator


-9*(x-1))

We multiply parentheses

-9x-

We add all the numbers together, and all the variables

-9x

Back to the equation:

-(-9x)


We get rid of parentheses

6x/((x-1)*(x-6)))+(+9x=0

We multiply all the terms by the denominator


6x+9x*((x-1)*(x-6)))+(=0