Sometimes you are presented with solving for unknown variables in rational expressions (expression where numerator and or denominator are polynomials).

example:

First, find least common denominators (lcd). Factor any denominators if possible. We can factor 2x-4 to 2(x-2). This happens to be our lcd. We’ll multiply the first term by 2 and the final term by 2x-4.

Now, let’s simplify by multiplying:

Let’s add terms on the right side:

Since the denominators are the same on both sides, the numerators mut be equal:

Then:

add 4 to both sides:

divide by 3 on both sides:

If you plug in 2 to both sides you’ll get undefined. **No solutions**.