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# Rational

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A rectangle has an area of ( 𝑥−3/ 𝑥+2 ) meters squared and a length of (9𝑥 − 3x^2 ) meters. Algebraically determine the width of the rectangle.

Thank you.

Jun 9, 2021

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If the area is (x-3)/(x-2) and the length is 9x-3x^2, then the width is (x-3/(x-2) divided by 9x-3x^2.

$$\frac{\frac{x-3}{x-2}}{9x-3x^2}=\frac{x-3}{\left(x-2\right)\left(9x-3x^2\right)}=\frac{x-3}{\left(x-2\right)\cdot \:3x\left(3-x\right)}=-\frac{1}{3x\left(x-2\right)}$$

JP

Jun 9, 2021