Question

Answer 1

`a, = (3x^2 + 5x - 4 - x^2 + 1 - x^2 + 9)/((x+3)(x-1))`

`= (x^2 + 5x + 6)/((x+3)(x-1))`

`= ((x+3)(x+2))/((x+3)(x-1))`

`= (x+2)/(x-1)`

`b, M = 0,5 => (x+2)/(x-1) = 0,5`

 

`=> x = 3`

 

Answer 2

`B13:`

`a)` Với `x \ne 1,x \ne -3` có:

`M=[3x^2+5x-4]/[(x+3)(x-1)]-[x+1]/[x+3]-[x+3]/[x-1]`

`M=[3x^2+5x-4-(x+1)(x-1)-(x+3)^2]/[(x+3)(x-1)]`

`M=[3x^2+5x-4-x^2+1-x^2-6x-9]/[(x+3)(x-1)]`

`M=[x^2-x-12]/[(x+3)(x-1)]`

`M=[(x+3)(x-4)]/[(x+3)(x-1)]=[x-4]/[x-1]`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`b)` Với `x \ne 1,x \ne -3` có:

`M=0,5<=>[x-4]/[x-1]=1/2<=>[x-4]/[x-1]-1/2=0`

                `<=>[2(x-4)-x+1]/[2(x-1)]=0`

                    `=>2x-8-x+1=0<=>x=7` (t/m)