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

(15x^{2} - 8x - 7)/(x^{2} - 2x +1).

GAMEMASTERX40
Oct 2, 2018

#1**+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

CPhill
Oct 2, 2018

#2**+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.

tertre
Oct 2, 2018