# How do you solve #x/(2x-6)=2/(x-4)#?

##### 1 Answer

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.

Check.

#### Explanation:

Given:

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:

Check:

This checks.