add: (5/x^2-x-6) + (4/x^2+4x+4)

Question

pleaseeeee help meee

Answer 1

OK, Robyn, you misunderstood what Jan was asking, so I'm going to assume I know what you are asking.

 

Assuming your first denominator is x² - x - 6 and the second is x² + 4x + 4, then you should type your equation...

 

5/(x2 - x - 6) + 4/(x2 + 4x + 4)

 

Otherwise, we don't know which part is your denominator and which are extra terms.

 

So, again, assuming that's what you mean, let's do this thing!

 

First, we have to factor each trinomial in your denominators.

 

We end up with 5/[(x -3)(x + 2)] + 4/[(x +2)(x + 2)]. Hopefully you can get that far without help.

 

Now, we have to find a common denominator in order to add.  Let's say we had 1/4 + 1/6.  If we break down 1/4, we get 1/(2 x 2), and if we break down 1/6, we get 1/(2 x 3).

 

What is missing from the 2 x 2 that is in the 2nd denominator? 3.  Multiplying 1/4 x 3/3 = 3/12.

 

What is missing from the 2 x 3 that is in the first denominator? Another 2.  Multiplying 1/6 x 2/2 = 2/12.

 

Then, we can add 3/12 + 2/12 = 5/12.

 

Now to find our common denominator!

 

OK, soooooo, we have two factors, both binomials, in each denominator.  

 

What's missing from the first that is in the 2nd?  Another x + 2, so we multiply 5/[(x -3)(x + 2)] x (x + 2)/(x + 2) = [5(x + 2)]/[(x -3)(x + 2)(x + 2)]

 

What's missing from the 2nd that's in the first? x -3, so we multiply 4/[(x +2)(x + 2)] x (x - 3)/(x - 3) = [4(x - 3)]/[(x +2)(x + 2)(x - 3)]

 

Putting that all together, we have [5(x + 2)]/[(x -3)(x + 2)(x + 2)] +  [4(x - 3)]/[(x +2)(x + 2)(x - 3)]

 

Since we now have a common denominator, we can add the numerators and put them over the same denominator.

 

[5(x + 2) + 4(x - 3)] / [(x +2)(x + 2)(x - 3)]

 

We have to distribute in the numerator, getting (5x + 10 + 4x - 12) / [(x +2)(x + 2)(x - 3)]

 

Combining like terms in the numerator, we get (9x - 2) / [(x +2)(x + 2)(x - 3)]

 

If we multiply the factors of the denominator, we get (9x - 2) / (x³  + x² - 8x - 12)

 

Hope this helps!!