First one: 3/4 = __/8
to get 8, they did 4*2
so whatever you do to the bottom, you do to the top
3*2=6
the first answer is - 3/4 = 6/8
the second one: 3/8 + 3/4
we need to find the LCD (Lowest Common Denominator)
3/8 = 8,16,
3/4= 4,8
the LCD is 8, now we just need to add the numerators
3/8 + 3/8 = 9/8
we could covert it into a mixed fraction
9/8 = 1 1/8
i hope this helped!!
Answer:
x= -11
Step-by-step explanation:
1/2(x-8)=3/2x+7
distribute
1/2x-4 = 3/2x+7
subtract 1/2x from both sides
1/2x cancels out
-4 = 1x+7
subtract 7 from both sides
-11 = 1x (1x is the same as "x")
We want to simplify:
![(\frac{1}{x+3}+ \frac{6}{ x^{2} +4x+3})* \frac{x+3}{x+1}](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B1%7D%7Bx%2B3%7D%2B%20%5Cfrac%7B6%7D%7B%20x%5E%7B2%7D%20%2B4x%2B3%7D%29%2A%20%5Cfrac%7Bx%2B3%7D%7Bx%2B1%7D%20)
first we factorize
![x^{2} +4x+3](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B4x%2B3)
as
![(x+3)(x+1)](https://tex.z-dn.net/?f=%28x%2B3%29%28x%2B1%29)
then multiply
![\frac{1}{x+3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%2B3%7D)
by
![\frac{x+1}{x+1}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%2B1%7D%7Bx%2B1%7D%20)
to equalize the denominators of the first expression, and add the fractions.
![(\frac{1}{x+3}*\frac{x+1}{x+1} + \frac{6}{(x+3)(x+1)})* \frac{x+3}{x+1}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7Bx%2B3%7D%2A%5Cfrac%7Bx%2B1%7D%7Bx%2B1%7D%20%2B%20%5Cfrac%7B6%7D%7B%28x%2B3%29%28x%2B1%29%7D%29%2A%20%5Cfrac%7Bx%2B3%7D%7Bx%2B1%7D%20)
![\frac{x+7}{(x+3)(x+1)}* \frac{x+3}{x+1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B7%7D%7B%28x%2B3%29%28x%2B1%29%7D%2A%20%5Cfrac%7Bx%2B3%7D%7Bx%2B1%7D)
simplify x+3:
![\frac{x+7}{(x+1)}* \frac{1}{x+1}= \frac{x+7}{ x^{2} +2x+1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B7%7D%7B%28x%2B1%29%7D%2A%20%5Cfrac%7B1%7D%7Bx%2B1%7D%3D%20%5Cfrac%7Bx%2B7%7D%7B%20x%5E%7B2%7D%20%2B2x%2B1%7D%20)
a.
![\frac{x+7}{ x^{2} +2x+1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B7%7D%7B%20x%5E%7B2%7D%20%2B2x%2B1%7D)
b.
steps already described
c.
x cannot be -1, nor -3 because the fractions with denominators (x+1) and (x+3) would not be defined.
X=1, because they both have the same height (y), so they'll cross each other!
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (4, 1) and (2, 5). Substitute:
![m=\dfrac{5-1}{2-4}=\dfrac{4}{-2}=-2](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B5-1%7D%7B2-4%7D%3D%5Cdfrac%7B4%7D%7B-2%7D%3D-2)
<h3>Answer: The slope is -2.</h3>