Question

Felipe and Ajay manipulated the rational expression \dfrac{-6y - 4}{-8y - 4}

−8y−4
−6y−4
​
start fraction, minus, 6, y, minus, 4, divided by, minus, 8, y, minus, 4, end fraction. Their responses are shown below.
Felipe Ajay
\dfrac{3y+2}{2y+1}
2y+1
3y+2
​
start fraction, 3, y, plus, 2, divided by, 2, y, plus, 1, end fraction \dfrac{-6y}{-8y}
−8y
−6y
​
start fraction, minus, 6, y, divided by, minus, 8, y, end fraction
Which student wrote an expression that is equivalent to the original expression?

Answer 1

Neither of them

Explanation:

`(-6y-4)/(-8y-4) = (2(-3y-2))/(4(-2y-1)) = (-2(3y+2))/(-4(2y+1)) = (2(3y+2))/(4(2y+1))`

We can cancel this fraction and obtain:

`(3y+2)/(2(2y+1))`

So neither of them wrote an expression that is equivalent to the original expression. Felipe's expression is missing a 2 in the denominator.