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Sagot :
Given the expression that represents the length of the rectangle:
[tex]3x-4[/tex]And the expression that represents the area of the rectangle:
[tex]6x^4-8x^3+9x^2-3x-12[/tex]You need to remember that the formula for calculating the area of a rectangle is:
[tex]A=lw[/tex]Where "l" is the length and "w" is the width.
If you solve for the width, you get this formula:
[tex]w=\frac{A}{l}[/tex]Therefore, you can write this expression to represent the width of the given rectangle:
[tex]\frac{6x^4-8x^3+9x^2-3x-12}{3x-4}[/tex]In order to simplify it, you can follow these steps:
1. Rewrite this term in this form in the numerator:
[tex]3x=-12x+9x[/tex]Then:
[tex]=\frac{6x^4-8x^3+9x^2-12x+9x-12}{3x-4}[/tex]2. Group pair of terms in the numerator and factor the Greatest Common Factor (the largest factor each group has in common) out of the parentheses:
[tex]=\frac{(6x^4-8x^3)+(9x^2-12x)+(9x-12)}{3x-4}[/tex][tex]=\frac{2x^3(3x-4)+3x(3x-4)+3(3x-4)}{3x-4}[/tex]3. Factor this Greatest Common Factor out in the numerator:
[tex]3x-4[/tex]You get:
[tex]=\frac{(3x-4)(2x^3+3x+3)}{3x-4}[/tex]4. By definition:
[tex]\frac{a}{a}=1[/tex]Therefore, you get:
[tex]=2x^3+3x+3[/tex]Hence, the answer is:
[tex]2x^3+3x+3[/tex]
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