+73 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).
+129852 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
+4622 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.
