I'm assuming the function is f(x) = (2x+8)/(x^2+5x+6). If so, make sure to use parenthesis to indicate that you're dividing all of "2x+8" over all of "x^2+5x+6" as one big fraction. Otherwise, things are ambiguous and it leads to confusion.
Side Note: x^2 means "x squared"
Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)
There are no common factors between the numerator and denominator. So there is nothing to cancel out.
Recall that you cannot divide by zero. Something like 1/0 is undefined.
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3
The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.
3(4 - 2x) + 3x 12 + 3x 12 + 6x 12 - 3x 12 - 9x
12 - 6x + 3 • 12 + 3 • 12 + 6 • 12 - 3 • 12 - 9x
12 - 6x + 36 + 36 + 72 - 26 - 9x
-9x - 6x + 12 + 36 + 36 + 72 - 26
-15x + 156 - 26
-15x + 130
Steps to solve:
3 + 2x = -6x + 4
~Subtract 3 to both sides
3 - 3 + 2x = -6x + 4 - 3
~Simplify
2x = -6x + 1
~Add 6x to both sides
2x + 6x = -6x + 6x + 1
~Simplify
8x = 1
~Divide 8 to both sides
8x/8 = 1/8
~Simplify
x = 1/8
Best of Luck!
str(pi. n(digits=1000000))[1000000] using Sage.
A)
The dotted triangle is the transformed/new one and is smaller than the original figure so the dilation is a reduction.
b)
All points moved 1/3 of their distance to the center of the dilation/the origin
1-1/3=2/3 as a scale factor, or in other words if any of the original point coordinates gets multiplied by the factor 2/3 you will receive the transformed coordinates