X^2-2x-3/(x+2) help please

Question

I'm studying for my exam and can't seem to remember how to solve these types of problems can someone please guide me

 

x2 - 2x - 3/(x+2) It says to perform the indicated operation and simplify. Write your answer in standard form

Answer 1

The equation is likely (x² -2x -3)/(x+2) and to simplify you can do polynomial synthetic division or long division. Using long division because it works in all cases:

        ________

x+2√x² -2x -3             how many times does x go into x²  , x times

 

        x - 4 ______

x+2√x²  - 2x -3            multiply x by x + 2 and create the next row

      -(x² )

 

           -4x - 3             bring down the -3 and repeat first step. how many times does x go into -4x, -4 times

         -(-4x - 8)            multiply x + 2 by -4

                 

                    5             (this is the remainder but it must be in the form 5/(x+2)

 

so the answer is x - 4 + 5/(x + 2). Hopefully, this is what your teacher considers "simplified".

                          

 

 

 

 

Answer 2

Here are some general guidelines for simplifying rational expressions:

 

Step 1) Find the LCD.

 

Here the LCD is (x+2)

 

Step 2) Write equivalent fractions using the LCD.

 

Here we must remember that any non-fractional term can be made a fraction by putting it over one.  Note that multiplying the numerator and denominator by the same quantity gives an equivalent fraction.  Example 2/3 = (2*2)/(3*2) = 4/6

 

X² = x²/1 = x²(x+2)/(x+2) and 2x = 2x/1 = 2x(x+2)/(x+2)

 

Now we have

 

x²(x+2)/(x+2) - 2x(x+2)/(x+2) - 3/(x+2)

 

Step 3) Perform the operations across the top and put the result over the one LCD.

 

x²(x+2)-2x(x+2)-3 = x³+2x²-2x²-4x-3 = x³-4x-3

 

(x³-4x-3)/(x+2)

 

Step 4) Factor the numerator if possible and cancel common factors between numerator and denominator.

 

By looking at the numerator we see that x= -1 is a root so x+1 is a factor.  If a polynomial has rational roots you can also find them using the rational zeros theorem.  Most students find the factors using a graphing calculator.  Use caution when using a graphing calculator it can be misleading.  Using polynomial or synthetic division we find that our numerator factors into (x+1)(x²-x-3).  We factor the quadratic expression using the quadratic formula so our final result is

 

(x+1)(x-(1+sqrt(13))/2)(x-(1-sqrt(13))/2)/(x+2)

Answer 3

( x² -2x - 3 ) / ( x + 2)

 

Using long division

 

              x  -  4  Remainder 5

x + 2 √ x² - 2x - 3

            x² + 2x

 

                 - 4x - 3

                 - 4x - 8

 

                         5  is the remainder

 

Answer is: x - 4 + 5/ ( x + 2 )

Answer 4

You have to factor the numerator using the FOIL method and then divide that result by the denominator.

 

Factoring the numerator we have (x-3)(x+1). Dividing that result by the denominator, we have (x-3)(x+1)/(x+2).

 

 

Answer 5

I would assume that this is synthetic division. Therefore you would set up (x+2) as -2 and put that in a box. Then your coefficients for the numerator are 1, -2, -3. Your bring the 1 down below the line and multiply it by -2.

 

1(-2) = -2 then add that answer to -2 which gives you -4.

-4(-2) = 8 then add that answer to -3 which gives you 5.

 

The final answer would be 1X - 4 + 5/(x+2) or X - 4 + 5/(x+2)

Answer 6

x² - 2x - 3/(x+2)  Mult. by (x + 2) to get a common den.

           

 

[x² (x + 2) - 2x(x + 2)  - 3]/(x + 2)

             

 

[x³ + 2x² - 2x² - 4x - 3]/(x + 2)

           

 

(x³ - 4x - 3)/(x + 2)