Answer:
a. A = -1 and B = 1
b. A = 7 and B = -5
Step-by-step explanation:
a.
![\frac{A}{x+1} +\frac{B}{x-1} = \frac{2}{x^2-1}](https://tex.z-dn.net/?f=%5Cfrac%7BA%7D%7Bx%2B1%7D%20%2B%5Cfrac%7BB%7D%7Bx-1%7D%20%20%3D%20%5Cfrac%7B2%7D%7Bx%5E2-1%7D)
![\frac{A*(x-1)+B*(x+1)}{(x+1)*(x-1)} = \frac{2}{x^2-1}](https://tex.z-dn.net/?f=%5Cfrac%7BA%2A%28x-1%29%2BB%2A%28x%2B1%29%7D%7B%28x%2B1%29%2A%28x-1%29%7D%20%3D%20%5Cfrac%7B2%7D%7Bx%5E2-1%7D)
![\frac{Ax - A + Bx + B}{x^2 -1} = \frac{2}{x^2-1}](https://tex.z-dn.net/?f=%5Cfrac%7BAx%20-%20A%20%2B%20Bx%20%2B%20B%7D%7Bx%5E2%20-1%7D%20%3D%20%5Cfrac%7B2%7D%7Bx%5E2-1%7D)
To the equation be true, the "x-parts" and "nonx-parts" mist be the same, so:
Ax + Bx = 0
(A + B)x = 0
A + B = 0
A = -B
B - A = 2
B - (-B) = 2
2B = 2
B = 1 and A = -1
b.
![\frac{A}{x+3} + \frac{B}{x +2} = \frac{2x -1}{x^2+5x+6}](https://tex.z-dn.net/?f=%5Cfrac%7BA%7D%7Bx%2B3%7D%20%2B%20%5Cfrac%7BB%7D%7Bx%20%2B2%7D%20%3D%20%5Cfrac%7B2x%20-1%7D%7Bx%5E2%2B5x%2B6%7D)
![\frac{A*(x+2) + B*(x+3)}{(x+3)*(x+2)} = \frac{2x-1}{x^2+5x+6}](https://tex.z-dn.net/?f=%5Cfrac%7BA%2A%28x%2B2%29%20%2B%20B%2A%28x%2B3%29%7D%7B%28x%2B3%29%2A%28x%2B2%29%7D%20%3D%20%5Cfrac%7B2x-1%7D%7Bx%5E2%2B5x%2B6%7D)
![\frac{Ax + 2A + Bx + 3B}{x^2 + 5x + 6} = \frac{2x-1}{x^2+5x+6}](https://tex.z-dn.net/?f=%5Cfrac%7BAx%20%2B%202A%20%2B%20Bx%20%2B%203B%7D%7Bx%5E2%20%2B%205x%20%2B%206%7D%20%3D%20%5Cfrac%7B2x-1%7D%7Bx%5E2%2B5x%2B6%7D)
To the equation be true, the "x-parts" and "nonx-parts" mist be the same, so:
Ax + Bx = 2x
(A + B)x = 2x
A + B = 2
A = 2 - B
2A + 3B = -1
2*(2-B) + 3B = -1
4 - 2B + 3B = -1
B = -5 and A = 2 - (-5) = 7
Step-by-step explanation:
"Solutions to the equation" just means that they are points on the line. To find out if these two points land on this line, plug each one in, like this:
1.5 = (1/4)(1) + (5/4)
1.5 = (1/4) + (5/4)
1.5 = (6/4)
1.5 = 1.5
Since the expression is true, this point is on the line.
Do the same process for the second point (remember a point is formatted (x,y)) and see if it is also a point on the line.
To find the x-intercept, simply plug in 0 for y and see what you get. It should look like (x,0).
Hello!
2y(4-x)=x/2
<span>[plug in 2 for x] </span>
<span>2y(4-2)=2/2 </span>
<span>[4-2 is 2, 2/2 is 1] </span>
<span>2y(2)=1 </span>
<span>[divide both sides by 2] </span>
<span>2y=1/2 </span>
<span>[divide by 2 again] </span>
<span>y=1/4
</span>
====>So As Result As We See, y = 1/4.<====
Hope this Helps! Have A WONDERFUL Rest Of Your Day! :)
(Ps. Don't Forget To Mark As BRAINLIEST!)
3.2
Step-by-step explanation:
we move the 8 to the other side by ×8
then 6÷15×8=M
M=3.2