How do you simplify (x+2/x-4) + (x/x+1)

Question

How do you simplify (x+2/x-4) + (x/x+1)

Answer 1

First, you will need a common denominator.

 

1) multiple the top and bottom of the first expression by (x+1): 

    

     [(x+2) * (x+1)] / [ (x-4) * (x+1) ]

 

2) multiply top and bottom of the second expression by (x-4):

 

    [ x  * (x-4) ] / [ (x+1) * (x-4) ]

 

As you can see, the two expressions have the same denominator now. So we are able to add them.

 

 

I am going to ignore the denominator for now since that will stay until the end (unless you would like to expand it which is not necessary).

 

The numerator would be:  (x+2)(x+1)+x(x-4) = [(x^2)+x+2x+2] + [(x^2)-4x]

 

simplifying you will get:   2*(x^2) -x+2

 

so the final answer would be: [2*(x^2) -x+2] / [(x+1)*(x-4)]

Answer 2

Hi Leah! The first step here will be two combine the two fractions, and to do that we will need the denominators to be equal.

 

A question for you first... If you multiply any number by 1/1 does it change the value of the number? No, of course not. Anything multiplied by 1 is it's original value. We will use this principle and multiple each fraction by the other fractions denominator on both the top and bottom.

 

((x+2)(x+1)) / ((x-4)(x+1)) + ((x)(x-4)) / ((x+1)(x-4))

 

You should notice that both fractions now have the same denominator, so now you can add them together. Can you simplify it from here? Keep in mind that it might be able to simplify further after you add the two together.