The area of a rectangle is expressed as
x^2 - 3x + 2
______________
2x^2 - 7x + 3
Determine its length if its width is:
x^2 - x - 2
______________
2x^2 - 3x - 2
Thank you so much!! :))
length = area / width
(x^2 - 3x + 2)/(2x^2 - 7x + 3) ÷ ((x^2 - 3x - 2)/(2x^2 - 3x - 2))
= (x^2 - 3x + 2)/(2x^2 - 7x + 3) * ((2x^2 - 3x - 2)/(x^2 - 3x - 2)
again , factor it
= (x-2)(x-1)/((x-3)(2x-1)) * (2x+1)(x-2)/((x-2)(x+1))
= ....
what's the answer? sorry i still find it hard to find the answer :\
To determine the length of the rectangle, we need to simplify the given expression for the area, and then find the quotient when dividing it by the given width expression. Let's go step by step:
Step 1: Simplify the area expression:
The area of a rectangle is given by length times width. Therefore, the area expression is the product of the provided expressions for length and width. Multiply the numerators and denominators together:
(x^2 - 3x + 2) / (2x^2 - 7x + 3) * (x^2 - x - 2) / (2x^2 - 3x - 2)
Step 2: Factor the numerator and denominator expressions:
(x - 2)(x - 1) / (2x - 1)(x - 3) * (x - 2)(x + 1) / (2x + 1)(x - 2)
Step 3: Cancel out common factors:
After factoring, we can see that (x - 2) is common in both the numerator and the denominator. Cancelling common factors, we have:
(x - 1) / (2x - 1)(x - 3) * (x + 1) / (2x + 1)
Step 4: Divide the simplified area expression by the width expression:
To find the length, divide the simplified area expression by the width expression:
(x - 1) * (x + 1) / [(2x - 1)(x - 3) * (2x + 1)]
Therefore, the length of the rectangle is:
(x - 1) * (x + 1) / [(2x - 1)(x - 3) * (2x + 1)]
Note: This is the simplified expression for the length based on the given width expression.
To determine the length of the rectangle, we divide the area formula by the width formula. By simplifying the resulting expression, we can find the length.
Given:
Area = (x^2 - 3x + 2) / (2x^2 - 7x + 3)
Width = (x^2 - x - 2) / (2x^2 - 3x - 2)
To find the length, we divide the Area by the Width:
Length = Area / Width
Substituting the given formulas:
Length = [(x^2 - 3x + 2) / (2x^2 - 7x + 3)] / [(x^2 - x - 2) / (2x^2 - 3x - 2)]
To divide fractions, we multiply the first fraction by the reciprocal of the second:
Length = [(x^2 - 3x + 2) / (2x^2 - 7x + 3)] * [(2x^2 - 3x - 2) / (x^2 - x - 2)]
Next, we factor both numerators and denominators:
Length = [((x - 2)(x - 1))/(2x - 1)(x - 3)(x - 1)] * [(2x + 1)(x - 2)/((x + 1)(x - 2)(x + 1))]
Some terms cancel out:
Length = (x - 1) / (2x - 1)
Therefore, the length of the rectangle is (x - 1) / (2x - 1).