Đáp án:
`a) 5x - 14,b) (x^3 - 2x^2 - 3x + 18)/[x(x + 3)(x - 3)] , c) [-5(x + 1)]/[4(x + 3)]`
Giải thích các bước giải:
`a) (x - 7)(4x - 5) - (2x - 7)^2`
`= 4x^2 - 5x - 28x + 35 - [(2x)^2 - 2.2x.7 + 7^2]`
`=4x^2 - 5x - 28x + 35 - (4x^2 - 28x + 49) = 4x^2 - 33x + 35 - 4x^2 + 28x - 49= -5x-14`
b) `18/(x^3 - 9x) - (2 - x)/(x + 3) + 3/(3 - x)`
`= 18/[x(x^2 - 9)] - (2 - x)/(x + 3) + 3/(3 - x)`
`=18/[x(x + 3)(x - 3)] - (2 - x)/(x + 3) + 3/(3 - x)`
`= 18/[x(x + 3)(x - 3)] - (2 - x)/(x + 3) + -3/(x - 3)`
`= 18/[x(x + 3)(x - 3)] - [(2 - x).x(x - 3)]/[x(x + 3)(x - 3)] + [-3.x(x + 3)] /[x(x + 3)(x - 3)]`
`= [18 - ((2 - x).x(x - 3)) + [-3.x(x + 3)]]/[x(x + 3)(x - 3)]`
`= [18 - ((2 - x).(x^2 - 3x)) + (-3x^2 - 9x))/[x(x + 3)(x - 3)]`
`= [18 - (2x^2 - 6x - x^3) + 3x^2 - 3x^2 - 9x]/[x(x + 3)(x - 3)]`
`= [18 - 2x^2 + 6x + x^3 + 3x^2 - 3x^2 - 9x]/[x(x + 3)(x - 3)]`
`=(x^3 - 2x^2 - 3x + 18)/[x(x + 3)(x - 3)]`
c) `(5x - 15)/(4x + 4) : (9 - x^2)/(x^2 + 2x + 1)`
`= (5x - 15)/(4x + 4) . (x^2 + 2x + 1)/(9 - x^2)`
`= [5(x - 3)]/[4(x + 1)] . [(x + 1)^2]/[(3 - x)(x + 3)]`
`= [5(x - 3)(x + 1)^2]/[4(x+ 1 )(3 - x)(x + 3)]`
`= [-5(3 - x)(x+ 1 )^2]/[4(x+ 1 )(3 - x)(x + 3)]= [-5(x + 1)]/[4(x + 3)]`
