This week we learned how to add and subtract rational expressions. These are a bit harder than multiplying and dividing because the denominator has to be the same throughout the expression.

Steps to simplify:

1. determine lowest common denominator (LCD)
2. rewrite each fraction as an equivalent fraction with LCD
For example: $\frac{x-9}{2x}-\frac{3x}{x-4}$ where “x” cannot equal 0 or 4.
1. For this expression, the least common denominator would be $2x(x-4)$ because neither denominator can be simplified any farther or multipled to create a common denominator, so we multiple the two denominators together to create one LCD.
2. Since we’re multiplying the bottom, we also have to do the same to the top, so the equation becomes: $\frac{(x-9)(x-4)}{2x(x-4)}-\frac{(3x)(2x)}{(x-4)(2x)}$.
3. This simplifies to $\frac{x^2-13x+36-6x^2}{2x(x-4)}$
4. The final simplified expression will be $\frac{-5x^2-13x+36}{2x(x-4)}$