25 point for this question:

for which values of a and b the following is true for any real number x?
[tex](x-4)/x^2+7x-18=a/x+9+b/x-2[/t ex]

a=   b =

Step-by-step explanation:

Given,

= +

Now take  lcm on right hand side

=

By equating coefficients of respective terms

x-4 = a(x-2)+b(x+9)

a+b=1  -----1 ; 9b-2a=-4  -----2

Substitute b=1-a in 2

9(1-a)-2a=-4

11a=9+4=13

a=

As b=1-a=1- =

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4

a

step-by-step explanation: