The area of a rectangle is 16. The length is x^5/ (x+1) and the width is ( x+1)/ x^3 . what is x?

Given that the length of the rectangle ( L ) = x^5/
(x+1)

Also, given that the width ( w) = (x+1)/
x^3

We need to determine (x) such that the area of the
rectangle is 16 square units.

We know that the area of the
rectangle (a) is:

a = Length * width = L*w =
16

==> [( x^5 / (x+ 1)] * [(x+1)/ x^3)] =
16

==> (x^5 ( x+ 1) / ( x+ 1) x^3 =
16

We will reduce similar
terms.

==> x^5 / x^3 =
16

From exponent properties we know that x^a/ x^b =
x^(a-b)

==> x^(5 - 3) =
16

==> x^2 = 16

Now we
will take the root for both sides:

==>
x= 4