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Ms.Sanchez is placing tiles on her bathroom floor. The area of the floor is 15x2 - 8x - 7 ft2. The area of one tile is x2 - 2x +1 ft2. To find the number of tiles needed, simplify the rational expression:

(15x2 - 8x - 7)/(x2 - 2x +1).

 Oct 2, 2018
edited by GAMEMASTERX40  Oct 2, 2018
 #1
avatar+96067 
+4

15x^2 - 8x - 7   factors as  (15x + 7) (x - 1)

 

x^2 - 2x + 1   factors as  ( x - 1) (x - 1)

 

So we have

 

[ (15x + 7) (x - 1) ] / [ ( x - 1) (x - 1)  ]      ...cancel the  x - 1  factors on top/bottom and we have

 

[15x + 7 ]  / [ x - 1 ]    =    tiles needed

 

 

cool cool cool

 Oct 2, 2018
 #2
avatar+3836 
+4

I don't know if this is a good way to do this, but...

First, you can factor the numerator, which is \(15x^2-8x-7\), to \(\left(x-1\right)\left(15x+7\right)\).

We can do the same thing with the denominator \(\:x^2-2x+1\), to \(\left(x-1\right)^2.\)

Now, we have \(\frac{\left(x-1\right)\left(15x+7\right)}{\left(x-1\right)^2}\). And, we can cancel \(x-1\), since that is our common factor. Thus, we are left with \(\boxed{\frac{15x+7}{x-1}}\).

 

If you need more explanation on the factoring, just tell me. Also, I think synthetic division works.

smileysmiley

 Oct 2, 2018

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