Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. VIEW FILE ATTACHED

Answer 1

Answer: see below

Explanation:

`P(x)=(2)/(3x-1)\qquad \qquad Q(x)=(6)/(-3x+2)\\`

P(x) ÷ Q(x)

`(2)/(3x-1)/ (6)/(-3x+2)\\\\\\=(2)/(3x-1)* (-3x+2)/(6)\\\\\\=\large\boxed{(-3x+2)/(3(3x-1))}`

P(x) + Q(x)

`(2)/(3x-1)+ (6)/(-3x+2)\\\\\\=(2)/(3x-1)\bigg((-3x+2)/(-3x+2)\bigg)+ (6)/(-3x+2)\bigg((3x-1)/(3x-1)\bigg)\\\\\\=(2(-3x+2)+6(3x-1))/((3x-1)(-3x+2))\\\\\\=(-6x+4+18x-6)/((3x-1)(-3x+2))\\\\\\=(12x-2)/((3x-1)(-3x+2))\\\\\\=\large\boxed{(2(6x-1))/((3x-1)(-3x+2))}`

P(x) - Q(x)

`(2)/(3x-1)- (6)/(-3x+2)\\\\\\=(2)/(3x-1)\bigg((-3x+2)/(-3x+2)\bigg)- (6)/(-3x+2)\bigg((3x-1)/(3x-1)\bigg)\\\\\\=(2(-3x+2)-6(3x-1))/((3x-1)(-3x+2))\\\\\\=(-6x+4-18x+6)/((3x-1)(-3x+2))\\\\\\=(-24x+10)/((3x-1)(-3x+2))\\\\\\=\large\boxed{(-2(12x-5))/((3x-1)(-3x+2))}`

P(x) · Q(x)

`(2)/(3x-1)* (6)/(-3x+2)\\\\\\=\large\boxed{(12)/((3x-1)(-3x+2))}`