Answer:
We conclude that:
![\frac{x+2}{x+4}-\frac{x-1}{x+6}=\frac{5x+16}{\left(x+4\right)\left(x+6\right)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7Bx%2B4%7D-%5Cfrac%7Bx-1%7D%7Bx%2B6%7D%3D%5Cfrac%7B5x%2B16%7D%7B%5Cleft%28x%2B4%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D)
Step-by-step explanation:
Given the expression
![\frac{x+2}{x+4}-\frac{x-1}{x+6}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7Bx%2B4%7D-%5Cfrac%7Bx-1%7D%7Bx%2B6%7D)
Least Common Multiple of x+4, x+6: (x+4) (x+6)
Adjusting fractions based on the LCM
![=\frac{\left(x+2\right)\left(x+6\right)}{\left(x+4\right)\left(x+6\right)}-\frac{\left(x-1\right)\left(x+4\right)}{\left(x+6\right)\left(x+4\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cleft%28x%2B2%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D%7B%5Cleft%28x%2B4%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D-%5Cfrac%7B%5Cleft%28x-1%5Cright%29%5Cleft%28x%2B4%5Cright%29%7D%7B%5Cleft%28x%2B6%5Cright%29%5Cleft%28x%2B4%5Cright%29%7D)
since the denominators are equal, combine the fractions:
![\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bc%7D%5Cpm%20%5Cfrac%7Bb%7D%7Bc%7D%3D%5Cfrac%7Ba%5Cpm%20%5C%3Ab%7D%7Bc%7D)
so the expression becomes
![=\frac{\left(x+2\right)\left(x+6\right)-\left(x-1\right)\left(x+4\right)}{\left(x+4\right)\left(x+6\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Cleft%28x%2B2%5Cright%29%5Cleft%28x%2B6%5Cright%29-%5Cleft%28x-1%5Cright%29%5Cleft%28x%2B4%5Cright%29%7D%7B%5Cleft%28x%2B4%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D)
![=\frac{x^2+8x+12-\left(x-1\right)\left(x+4\right)}{\left(x+4\right)\left(x+6\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%5E2%2B8x%2B12-%5Cleft%28x-1%5Cright%29%5Cleft%28x%2B4%5Cright%29%7D%7B%5Cleft%28x%2B4%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D)
![=\frac{x^2+8x+12-x^2-3x+4}{\left(x+4\right)\left(x+6\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%5E2%2B8x%2B12-x%5E2-3x%2B4%7D%7B%5Cleft%28x%2B4%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D)
simplify
![=\frac{5x+16}{\left(x+4\right)\left(x+6\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5x%2B16%7D%7B%5Cleft%28x%2B4%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D)
Therefore, we conclude that:
![\frac{x+2}{x+4}-\frac{x-1}{x+6}=\frac{5x+16}{\left(x+4\right)\left(x+6\right)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7Bx%2B4%7D-%5Cfrac%7Bx-1%7D%7Bx%2B6%7D%3D%5Cfrac%7B5x%2B16%7D%7B%5Cleft%28x%2B4%5Cright%29%5Cleft%28x%2B6%5Cright%29%7D)
Answer:
The equation of the line is:
![y=(-\frac{1}{2})x+1](https://tex.z-dn.net/?f=y%3D%28-%5Cfrac%7B1%7D%7B2%7D%29x%2B1)
Therefore, option a is the correct answer.
Step-by-step explanation:
Given the points
Finding the slope
![\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%5C%3Abetween%5C%3Atwo%5C%3Apoints%7D%3A%5Cquad%20%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(-2,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:-1\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%28-2%2C%5C%3A2%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%284%2C%5C%3A-1%5Cright%29)
![m=\frac{-1-2}{4-\left(-2\right)}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-1-2%7D%7B4-%5Cleft%28-2%5Cright%29%7D)
![m=-\frac{1}{2}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7B2%7D)
As the point-slope form of the equation of the line is
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
where m is the slope
substituting the values
and the point (-2, 2)
![y-y_1=m\left(x-x_1\right)](https://tex.z-dn.net/?f=y-y_1%3Dm%5Cleft%28x-x_1%5Cright%29)
![y-2=\frac{-1}{2}\left(x-\left(-2\right)\right)](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7B-1%7D%7B2%7D%5Cleft%28x-%5Cleft%28-2%5Cright%29%5Cright%29)
![y-2=\frac{-1}{2}\left(x+2\right)](https://tex.z-dn.net/?f=y-2%3D%5Cfrac%7B-1%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29)
∵![\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3Afraction%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7B-a%7D%7Bb%7D%3D-%5Cfrac%7Ba%7D%7Bb%7D)
Add 2 to both sides
![y-2+2=-\frac{1}{2}\left(x+2\right)+2](https://tex.z-dn.net/?f=y-2%2B2%3D-%5Cfrac%7B1%7D%7B2%7D%5Cleft%28x%2B2%5Cright%29%2B2)
![y=(-\frac{1}{2})x+1](https://tex.z-dn.net/?f=y%3D%28-%5Cfrac%7B1%7D%7B2%7D%29x%2B1)
Hence, the equation of the line is:
![y=(-\frac{1}{2})x+1](https://tex.z-dn.net/?f=y%3D%28-%5Cfrac%7B1%7D%7B2%7D%29x%2B1)
Therefore, option a is the correct answer.
Slope is the change in Y over the change in X:
Slope = (1 - -5) / 4 -1)
Slope = 6/3 = 2
Answer:
where is part b?
Step-by-step explanation:
can i see a picture of part b?
If point R(6, 2) is rotated 180 degrees clockwise about the origin, the new point would be R'(-6, -2)
<h3>What is a transformation?</h3>
Transformation is the movement of a point from its initial location to a new location. Types of transformations are r<em>eflection, translation, rotation and dilation.</em>
Rigid transformation are transformation that preserve the shape and size hence producing congruent figures such as translation, reflection and rotation.
If point R(6, 2) is rotated 180 degrees clockwise about the origin, the new point would be R'(-6, -2)
Find out more on transformation at: brainly.com/question/4289712
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