2a) Simplify the expressions for A and B, where A=x+4/xsquared+9x+20 and B= 3xsquared-9x/xsquared+3x-18

Question

b) Are the two expressions equivalent? Justify your answer.
c) Determine
i) A-B
ii) A•B
iii) B÷A

Answer 1

you probably meant:
A= (x+4)/(xsquared+9x+20)
= (x+4)/((x+4)(x+5))
= 1/(x+5) , x ≠ -4

B = (3xsquared-9x)/(xsquared+3x-18)
= 3x(x - 3)/((x+6)(x-3))
= 3x/(x+6) , x ≠ 3

clearly they are not equivalent

I am sure you can handle the algebra from this point.