Adding Rational Expressions

Q:  Add x/(x+1) + 2x/(x+1)

also, identify any x-values for which the expression is undefined.

Answer:  In order to add rational expressions, you need common denominators.  These expressions already have a common denominator of (x+1) so the hard work is done.

You can just add the numerators together and combine the fraction (leave the denominator alone) to get:

x/(x+1) + 2x/(x+1) = (x + 2x) /(x+1) = 3x / (x + 1) [final answer]

Now, we need to identify any x-values for which the expression is undefined.  We need to know that you can never divide by 0, so the denominator of any rational expression can never equal 0.

So, look at the denominator and find where it equals 0:

x+1 = 0

Solve for x to get:

x = -1

Therefore, the denominator is 0 if x = -1.  This tells us that x can never be -1.  The problem is undefined when x = -1.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s