Question

Thực hiện phép tính

a) \(\dfrac{x^2}{3x+6}\)+ \(\dfrac{4x+4}{3x+6}\)

b) \(\dfrac{2}{x}\)+ \(\dfrac{3}{x+1}\) - \(\dfrac{10x+7}{x.\left(x+1\right)}\)

c) x\(^2\) - 3. (x - 5) - 25 = 0

Answer 1

`(x^2)/(3x+6) + (4x+4)/(3x+6)`

`= (x^2 + 4x + 4)/(3x+6)`

`= (x+2)^2/(3*(x+2))`

`= (x+2)/3`

`2/x + 3/(x+1) - (10x + 7)/(x*(x+1))`

`= (2x + 2)/(x*(x+1)) + (3x)/(x*(x+1)) - (10x + 7)/x*(x+1))`

`= (2x+2 +3x -10x - 7)/(x*(x+1))`

`= (-5x - 5)/(x*(x+1))`

`= (-5*(x+1))/(x*(x+1))`

`= -5/x`

`x^2 - 3*(x-5) - 25=0`

`=> x^2 - 3x +15 - 25 = 0`

`=>x^2 -3x -10 = 0`

`=>x^2 -5x +2x - 10 = 0`

`=> x(x-5) + 2(x-5) = 0`

`=> (x+2)(x-5) = 0`

TH1:

`x+2 = 0`

`=> x =-2`

TH2:

`x-5=0`

`=> x=5`