Answer:
w = (3x - 6)(x + 2) / 2(x + 5)(x + 4)
Explanation:
To find the width of the rectangle, we need to use the formula for the area of a rectangle:
Area = length x width
We are given that the area of the rectangle is:
3x³ - 9x² - 12x
And the length of the rectangle is:
2x³ + 18x² + 40x
So we can substitute these values into the formula to get:
3x³ - 9x² - 12x = (2x³ + 18x² + 40x) x width
Expanding the right side of the equation, we get:
3x³ - 9x² - 12x = 2x³ x width + 18x² x width + 40x x width
Simplifying the terms on the right side, we get:
3x³ - 9x² - 12x = (2x³ + 18x² + 40x)w
Dividing both sides by (2x³ + 18x² + 40x), we get:
w = (3x³ - 9x² - 12x) / (2x³ + 18x² + 40x)
Factoring out x from the terms in the numerator and denominator, we get:
w = x(3x² - 9x - 12) / 2x(x² + 9x + 20)
Simplifying the expression, we get:
w = (3x² - 9x - 12) / 2(x² + 9x + 20)
Now, we can factor the numerator and denominator to get:
w = (3x - 6)(x + 2) / 2(x + 5)(x + 4)
Therefore, the width of the rectangle is:
w = (3x - 6)(x + 2) / 2(x + 5)(x + 4)