Find constants a  and b  such that for all x  such that   and . give your answer as the ordered pair (a, b).

answer: (3,-2)

explanation

getting a common denominator on the right-hand side, we get

since both sides of the equation have the same denominators, we can multiply both sides by to cancel them out.

expanding out, we get

on the right-hand side, move all the x terms together (ax and bx) and all the constant terms together (a and -2b are constant terms)

we see that

for this identity to be true, the coefficient on x on the left-hand side must be equal to the coefficient of x on the right-hand side, and the constants must be equal. this gives us a system of equations

subtracting (ii) from (i) gives us

using , we find that .

therefore, a = 3 and b = -2 so (3,-2) is the answer

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3