Takumi and Kaliska manipulated the rational expression \dfrac{-9y^2 - 3y}{-6y^2 - 6y}

−6y

2

−6y

−9y

2

−3y



start fraction, minus, 9, y, squared, minus, 3, y, divided by, minus, 6, y, squared, minus, 6, y, end fraction. Their responses are shown below.

Takumi Kaliska

\dfrac{-3y(3y+1)}{-6y(y+1)}

−6y(y+1)

−3y(3y+1)



start fraction, minus, 3, y, left parenthesis, 3, y, plus, 1, right parenthesis, divided by, minus, 6, y, left parenthesis, y, plus, 1, right parenthesis, end fraction \dfrac{3y+1}{2y+2}

2y+2

3y+1



start fraction, 3, y, plus, 1, divided by, 2, y, plus, 2, end fraction

Both Takumi and Kaliska expression is equivalent to the original expression.

Step-by-step explanation:

Given : Takumi and Kaliska manipulated the rational expression

Takumi                                                    Kaliska

To find : Which student write an expression that is equivalent to the original expression ?

Solution :

Simplifying the rational expression,

Taking common term out,

Cancel the like terms in numerator and denominator,

On simplifying we see that both Takumi and Kaliska expression is equivalent to given expression.

Therefore, Both Takumi and Kaliska expression is equivalent to the original expression.

yes. we do proportions in probabilities.

the answer is b