How do you solve #x/(2x-6)=2/(x-4)#?
Restrict the domain so that the solutions do not cause division by zero in the original equation.
Multiply both sides by both denominators.
Solve the resulting quadratic.
Restrict the values of x so that any solutions that would cause division by zero are discarded:
Multiply both sides of the equation by
Please observe how the factors cancel:
Here is the equation with the cancelled factor removed:
Use the distributive property on both sides:
We can put the quadratic into standard form by adding
This factors and the restrictions can be dropped: