Find the area of a rectangle and simplify.
Width is x^2-8x+16/4x^2
Length is 2x^2-10x/x^2-9x+20
so close!
[2x / (x - 4)] * [(x - 4)^2 / 4x^2] = (x-4) / 2x
Apologies for the oversight. Thank you for pointing out the error.
The correct simplified area of the rectangle is:
Area = (x - 4) / 2x
To find the area of a rectangle, we multiply the length by the width.
Area = length * width
Area = [2x^2 - 10x / x^2 - 9x + 20] * [x^2 - 8x + 16 / 4x^2]
Now, let's simplify each part separately.
Simplifying the length:
2x^2 - 10x / x^2 - 9x + 20
= 2x(x - 5) / (x - 5)(x - 4)
= 2x / (x - 4)
Simplifying the width:
x^2 - 8x + 16 / 4x^2
= (x - 4)(x - 4) / 4x^2
= (x - 4)^2 / 4x^2
Now, plug these simplified forms back into the calculation for Area:
Area = [2x / (x - 4)] * [(x - 4)^2 / 4x^2]
= 2(x - 4) / 4
= (x - 4) / 2
So, the area of the rectangle is (x - 4) / 2, which is the simplified form.