The area of a rectangle is #(x^4+4x^3+ 3x^2-4x-4)#, and the length of the rectangle is #(x^3 +5x^2 +8x+ 4)#. If area length x width, what is the width of the rectangle?
1 Answer
Dec 28, 2016
Explanation:
The width is given by the rational expression:
#(x^4+4x^3+3x^2-4x-4)/(x^3+5x^2+8x+4)#
Let us see if we can simplify the expression:
Note that
#1+4+3-4-4 = 0#
So
#x^4+4x^3+3x^2-4x+4 = (x-1)(x^3+5x^2+8x+4)#
So:
#(x^4+4x^3+3x^2-4x-4)/(x^3+5x^2+8x+4) = x-1#