Đáp án:
`a) 3/4 , b) (x + 3)/(x - 3) , c) x in {4;2;5;1;7;-1}`
Giải thích các bước giải:
a) Thay x = 5 ta có :
`A = (x + 1)/(x + 3) = (5 + 1)/(5 + 3) = 6/8 = 3/4`
b) `B = 3/(x - 3) - (6x)/(9 - x^2) + x/(x + 3)`
`B = 3/(x- 3) - (-6x)/(x^2 - 9) + x/(x + 3)`
`B = 3/(x - 3) - (-6x)/[(x + 3)(x - 3)] + x/(x + 3) = [3(x + 3)]/[(x + 3)(x - 3)] + (6x)/[(x + 3)(x - 3)] + [x(x - 3)]/[(x + 3)(x - 3)]`
`= [3(x + 3) + 6x + x(x - 3)]/[(x + 3)(x - 3)] = (3x + 9 + 6x + x^2 - 3x)/[(x + 3)(x - 3)] = (x^2 + 6x + 9)/[(x + 3)(x - 3)] `
`= [(x + 3)^2]/[(x + 3)(x - 3)] = (x + 3)/(x - 3)`
c) `P=A.B = (x + 1)/(x + 3) . (x + 3)/(x - 3) = (x + 1)/(x - 3)`
`(x + 1)/(x - 3) = (x - 3 + 4)/(x - 3) = 1 + 4/(x - 3)`
`4/(x - 3) => x - 3 in Ư(4) = {1;-1;2;-2;4;-4} `
`=> x in {4;2;5;1;7;-1}`
