Write the simplified expression, written in factored form, to represent the perimeter of the rectangle.
Length is x^2-5x/x-2 and width is 6/x-2
The perimeter of a rectangle is given by the formula P = 2(l + w).
Given that the length is x^2 - 5x/x - 2 and the width is 6/x - 2, the factored form of the equation for the perimeter would be:
P = 2[(x^2 - 5x)/(x - 2) + 6/(x - 2)]
Simplifying the expression, we get:
P = 2[(x(x - 5))/(x - 2) + 6/(x - 2)]
Therefore, the simplified expression, written in factored form, to represent the perimeter of the rectangle is 2[(x(x - 5))/(x - 2) + 6/(x - 2)].
Are you sure
Apologies for my mistake. Let me correct that:
Given that the length is \(\frac{x^2-5x}{x-2}\) and the width is \(\frac{6}{x-2}\), the perimeter of the rectangle, \(\text{P}\), is given by:
\[P = 2\left(\frac{x^2-5x}{x-2} + \frac{6}{x-2}\right)\]
To simplify the expression, we first need to find a common denominator:
\[P = 2\left(\frac{x^2-5x + 6}{x - 2}\right)\]
Now, we can factor the numerator \(x^2 - 5x + 6\):
\[P = 2\left(\frac{(x-2)(x-3)}{x-2}\right)\]
Simplifying further:
\[P = 2(x-3)\]
\[P = 2x - 6\]
Therefore, the simplified expression, in factored form, for the perimeter of the rectangle is \(2x - 6\).
That doesn't make sense
Apologies for the confusion in my previous responses. Let's correct it:
Given that the length is \(\frac{x^2-5x}{x-2}\) and the width is \(\frac{6}{x-2}\), the formula for the perimeter of a rectangle is:
\[ P = 2( \text{Length} + \text{Width}) \]
Substitute the length and width values:
\[ P = 2\left( \frac{x^2 - 5x}{x - 2} + \frac{6}{x - 2} \right) \]
Combine the fractions:
\[ P = 2\left( \frac{x^2 - 5x + 6}{x - 2} \right) \]
Factorize the numerator:
\[ P = 2\left( \frac{(x-2)(x-3)}{x-2} \right) \]
Cancel out the common factor:
\[ P = 2(x - 3) \]
\[ P = 2x - 6 \]
Therefore, the perimeter of the rectangle in factored form is \(2x - 6\).