Adding and Subtracting Rational Expressions

Hi everyone, Alex here with another blog post. I'd first like to start off with saying that I hope you all had a good weekend. Anyways on to math.

The first step to adding or subtraction rational expressions is to check for a common denominator and if there isn't one then you must make the denominators on both sides of the equation the same.

example 1)

The common denominator in this equation would be b.

so the next step is to re-write the equation like so:

next multiply (a-1) by the negative sign and re-write the equation once more:

Lastly just solve the equation:

To get this answer you start with 2a minus a, which equals to just a

Then you just leave the +1 and put the whole equation over b. Congratulations your equation is now in its simplest form.

Alright lets try another example, this time we will be adding, the steps involved are relatively the same so lets begin

so basically what your going to want to do with this equation is to simplify the numerator by factoring. In this case we will be factoring 2 out of the equation.

now what we have left to do here is devide the (x+4) Out of the Equation and then we a left with and answer of 2.

In this last example I will demonstrate what you do in the case of the denominators not being the same.

In this example you would use factoring on the denominator in order to make it the same on both sides.

the next step would be to combine like terms and rewrite the equation.

so the equation should look something like this, Next simplify and rewrite.

now from here we can factor the equation.

The last step is to divide out what you can and rewrite the equation.



There we are, and that's how you add and subtract rational expressions, I hope everyone who read this enjoyed it and learned something from it.