The partial fraction decomposition of latex: \frac{x-9}{x^2-3x-18} x − 9 x 2 − 3 x − 18 is latex: \frac{a}{x-6}+\frac{b}{x+3} a x − 6 + b x + 3 . find the numbers latex: a\: a and latex: b b . then, find the sum latex: a+b a + b , which is a whole number. enter that whole number as your answer.

Not entirely sure what the question is supposed to say, so here's my best guess.

First, find the partial fraction decomposition of

This is equal to

Multiply both sides by , so that

Notice that if , the term involving vanishes, so that

Then if , the term with vanishes and we get

So we have

I think the final answer is supposed to be , so you end up with 1.

what is all that apply?

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.