Đáp án:
`a) x^2 + 12`
`b) x/(x + 5)`
`c) a + 4`
`d) 1/(x - 3)`
Giải thích các bước giải:
`a) A = (x + 2)^2 + (x - 2)^2 - (x - 2)(x + 2)`
`=x^2 + 2.x.2 + 2^2 + x^2 - 2.x.2 + 2^2 - (x^2 - 4)`
`=x^2 + 4x + 4 + x^2 - 4x + 4 - x^2 + 4 = x^2 + 12`
`b) B = (x^2 - 5x)/(x^2 - 25) = [x(x-5)]/[(x+5)(x - 5)] = x/(x + 5)`
`c) C = a^2/(a - 4) + 16/(4 - a) = a^2/(a - 4) + (-16)/(a - 4) = (a^2 - 16)/(a - 4) = [(a + 4)(a - 4)]/(a - 4) = a + 4`
`d) D = 5/(x + 3) + 3/(x - 3) - (9 - 7x)/(9 - x^2) = 5/(x + 3) + 3/(x - 3) - [-(9 - 7x)]/[x^2 - 9]`
`= 5/(x + 3) + 3/(x - 3) - (7x - 9)/(x^2 - 9)`
`= 5/(x + 3) + 3/(x - 3) - (7x - 9)/[(x + 3)(x - 3)]`
`= [5(x - 3)]/[(x + 3)(x - 3)] + [3(x + 3)]/[(x + 3)(x - 3)] - (7x - 9)/[(x + 3)(x - 3)]`
`= [5(x - 3) + 3(x + 3) - 7x + 9]/[(x + 3)(x - 3)] = (5x - 15 + 3x + 9 - 7x + 9)/[(x + 3)(x - 3)`
`= (x + 3)/[(x + 3)(x - 3)] = 1/(x - 3)`
