Answer:
B
Step-by-step explanation:
Answer:
3rd option is correct
.........................................
So firstly, you want to multiply both sides by (x-2)(x+2) since it is the LCM, or lowest common multiplier. Your equation will look like this: ![\frac{3}{x+2} (x-2)(x+2)-\frac{4}{x-2} (x-2)(x+2)=5(x-2)(x+2)](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7Bx%2B2%7D%20%28x-2%29%28x%2B2%29-%5Cfrac%7B4%7D%7Bx-2%7D%20%28x-2%29%28x%2B2%29%3D5%28x-2%29%28x%2B2%29%20)
Next, you can cancel out the denominators on 3/x+2 and 4/x-2 on the left side: ![3(x-2)-4(x+2)=5(x-2)(x+2)](https://tex.z-dn.net/?f=%203%28x-2%29-4%28x%2B2%29%3D5%28x-2%29%28x%2B2%29%20)
Next, foil: ![3x-6-4x-8=5x^2-20](https://tex.z-dn.net/?f=%203x-6-4x-8%3D5x%5E2-20%20)
Next, combine like terms: ![-x-14=5x^2-20](https://tex.z-dn.net/?f=%20-x-14%3D5x%5E2-20%20)
Next, add x + 14 on both sides: ![0=5x^2+x-6](https://tex.z-dn.net/?f=%200%3D5x%5E2%2Bx-6%20)
Next, replace x with -5x + 6x: ![0=5x^2-5x+6x-6](https://tex.z-dn.net/?f=%200%3D5x%5E2-5x%2B6x-6%20)
Next, factor 5x^2-5x and 6x-6 separately. Make sure that both factors have the same quantity within the parentheses: ![0=5x(x-1)+6(x-1)](https://tex.z-dn.net/?f=%200%3D5x%28x-1%29%2B6%28x-1%29%20)
With this, we can rewrite it as
From here, we solve for x in (5x+6) and (x-1) separately and setting them to zero.
![5x+6=0\\ 5x=-6\\x=-\frac{6}{5} =-1.2](https://tex.z-dn.net/?f=%205x%2B6%3D0%5C%5C%205x%3D-6%5C%5Cx%3D-%5Cfrac%7B6%7D%7B5%7D%20%3D-1.2%20%20)
![x-1=0\\ x=1](https://tex.z-dn.net/?f=%20x-1%3D0%5C%5C%20x%3D1%20)
In short, x = -1.2, 1.
there are two expressions that can represent the length of the rectangle, these two expressions are:
L = x
or
L = (4x + 12)
<h3>
Which expression could represent the length of the rectangle?</h3>
Remember that for a rectangle of length L and width W, the area is given by:
A = L*W
In this case, we know that the area is:
![A = 4x^2 + 12x](https://tex.z-dn.net/?f=A%20%3D%204x%5E2%20%2B%2012x)
We can factorize that expression into:
![A = x*(4x + 12)](https://tex.z-dn.net/?f=A%20%3D%20x%2A%284x%20%2B%2012%29)
So there are two expressions that can represent the length of the rectangle, these two expressions are:
L = x
or
L = (4x + 12)
If you want to learn more about rectangles:
brainly.com/question/17297081
#SPJ1
Answer: OPTION B.
Step-by-step explanation:
1. By definition, the line intercepts the x-axis when y=0. Therefore, you must susbtitute y=0 into the equation of the line given in the problem and solve for x, as you can see below:
![0=3x+6\\-6=3x\\x=-2](https://tex.z-dn.net/?f=0%3D3x%2B6%5C%5C-6%3D3x%5C%5Cx%3D-2)
2. Knowing that the x-intercept of the line from the equation and is -2 and the x-intercept from the description is (0,0), you can conclude that the correct option is B.