Question

Match the products of rational expressions with their simplest forms. Tiles -3x^2/2y^2 x y^2/9x

5y^2 /10x^2 X 4x^2/y
9y^2/5x x -10x^2/3y
14x^2/5y x -10y/7x

Answer 1

#1 tiles goes with -1/6 x
#2 tiles goes with 2y
#3 tiles goes with 6xy
and #4 Tiles the last one goes with -4x

The tiles i start from left to right

Answer 2

`(-3x^2)/(2y^2) * (y^2)/(9x)=(-1)/(6)x`

`(5y^2)/(10x^2) * (4x^2)/(y)= 2y`

`(-9y^2)/(5x) * (-10x^2)/(3y)=6xy`

`(14x^2)/(5y) * (-10y)/(7x)=-4x`

Explanation:

(1)
`(-3x^2)/(2y^2) * (y^2)/(9x)`

cancel out y^2 at the top and bottom

x^2/x = x and -3/2*9 is -1/6

`(-3x^2)/(2y^2) * (y^2)/(9x)=(-1)/(6)x`

(2)
`(5y^2)/(10x^2) * (4x^2)/(y)`

y^2/y= y, x^2 cancelled out

5*10 / 4= 2

`(5y^2)/(10x^2) * (4x^2)/(y)= 2y`

(3)
`(-9y^2)/(5x) * (-10x^2)/(3y)`

x^2/x= x and y^2/y=y

90/15 =6

`(-9y^2)/(5x) * (-10x^2)/(3y)=6xy`

(4)
`(14x^2)/(5y) * (-10y)/(7x)`

x^2/x= x, cancel out y

14/7 = 2 , -10/5 = -2

`(14x^2)/(5y) * (-10y)/(7x)=-4x`