# How do you solve for x: #x/(x-3) = 3/(x-3) + 3 #?

##### 1 Answer

Aug 4, 2016

#### Explanation:

The first thing to do here is get rid of the denominators. Note that a possible solution to the original equation **must** satisfy the condition

#color(purple)(|bar(ul(color(white)(a/a)color(black)(x - 3 != 0 implies x != 3)color(white)(a/a)|)))#

So, to get rid of the denominators, multiply the last term by

#x/(x-3) = 3/(x-3) + 3 * (x-3)/(x-3)#

You can now focus exclusively on the **numerators**

#x = 3 + 3 * (x-3)#

Rearrange to get

#x = 3 + 3x - 9#

#x = 3x - 6#

#2x = 6 implies x = 6/2 = 3#

Notice that **one value** that it cannot take, i.e.

This means that your original equation has **no solution**,