Question

Find A and B if x+16=A(x+2)+B(2x-3) is an identity.

Answer 1

just replace x by 3/2 to get the value of A
replace x by -2 to get the value of B
what you get ?

Answer 2

Note when you put x=3/2, the term multiplied with B becomes 0
thats the reason you could find the value of A directly.

Answer 3

where did you get the 3/2?

Answer 4

yey! A=5
B=-2? right?

Answer 5

yes, thats correct :)
i got 3/2 from
2x-3 =0 ----> 2x=3---->x=3/2
because , to find A, i wanted the term with B=0, so i equated 2x-3 to 0, which eliminated B.

Answer 6

did you get that ^ ?

Answer 7

x+16=A(x+2)+B(2x-3)
x+16=Ax+2Bx+2A-3B
x+16=(A+2B)x+(2A-3B)
Therefore, (A+2B)x=x; 2A-3B=16
That is:
A+2B=1
2A-3B=16

so we got A=5 B=-2

Answer 8

@hartnn Thank you! :)