To find the width of the field, we divide the area of the field by its length:
Width = Area / Length
The area of the field is given by x^2+2x-15 meters, and the length is given by (x^2+3x-18)/(x+1) meters.
So, Width = (x^2+2x-15) / (x^2+3x-18)/(x+1)
To divide by a fraction, we can multiply by its reciprocal:
Width = (x^2+2x-15) * (x+1) / (x^2+3x-18)
Expanding both the numerator and denominator:
Width = (x^3 + x^2 + 2x^2 + 2x - 15x - 15) / (x^2 + 3x - 18)
Combining like terms in the numerator:
Width = (x^3 + 3x^2 - 13x - 15) / (x^2 + 3x - 18)
Now, let's simplify this expression further by using long division:
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x+3 | x^3 + 3x^2 -13x -15
- (x^3 + 3x^2 - 18x)
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5x + 3
Therefore, we have:
Width = x + 3 + (5x+3) / (x+3)
Simplifying, we get:
Width = x + 5 - (5/ (x+3))
The width of the field is x + 5 - (5/ (x+3)) meters.
Restrictions:
We need to consider restrictions that might result in division by zero. In this case, if x+3 equals zero, the divisor will become zero which is undefined. Therefore, x cannot equal -3.
So, the restriction is x ≠ -3.
a farmer has a field with area of x^2+2x-15 meters and a length of x^2+3x-18 over x+1 meters. what is the width of the field? simplify and state restrictions. Recall: a=l x w
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