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

Question

please help and provide a step by step if possible.

Answer 1

So the problem that you want to simplify is the following correct?

 

       (x+4)

       ------

       (x-1)

   ---------------

       (x²+x)

      -------

       (x-1)

 

Am I correct? If so, then okay... Let's get started.

 

1.  What we have here is fraction divided by a fraction. The first fraction being the following:

 

(x+4)

------

(x-1)

 

2. And the 2nd fraction being the following.

 

(x²+x)

-------

 (x-1)

 

3. WHENEVER you have a fraction divided by a fraction and you want to simplify, you take the first fraction and multiply by the reciprocal of the 2nd fraction. YOU WILL ALWAYS FOLLOW THIS RULE.

 

4.  So let's started in simplifying this bad boy fraction shall we?

 

take the first fraction:

(x+4)

------

(x-1)

 

NOW TAKE THE RECIPROCAL OF THE SECOND FRACTION AND MULTIPLY BY THE FIRST FRACTION:

(x+4)         (x-1)

------    *   --------

(x-1)         (x²+x)

 

5.  The (x+1) terms will cancel:

 

(x+4)          (x-1)

------    *    --------

(x-1)          (x²+x)

 

6.  And you get the following:

 

(x+4)

-------

(x²+x)

 

 

or if you decided to factor the bottom your answer could alternatively be:

  (x+4)

----------

[x(x+1)]

 

 

7. And That's it!

Answer 2

Anthony,

 

The equation can be written as

 

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

 

Cancelling out the x-1 term you have

(x+4)/(x^2+x)

or

(x+4)/(x(x+1))