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# Ms.Sanchez is placing tiles on her bathroom floor.

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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
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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   Oct 2, 2018
#2
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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.  Oct 2, 2018