Choose the correct rewriting of this algebraic fraction and give the exclusion represented by your choice.
4y(8y+24)^ - 1 : 2y/2y+3 OR y/(2)(y+3)?
y ≠ : +3 OR -3 ?
4y(8y+24)^ - 1 ,using the property that a^-x = 1/a^x
= 4y/(8y+24)
= 4y/(4(2y + 6) )
= y/(2y + 6)
or
y/(2(x+3)), since the denominator cannot be zero, x+3≠0 ----> x ≠ -3
Great, thank you so much! :)
Algebraic fraction simplify 8/y+4y
I would go with the rewriting y/(2)(y+3), which means y ≠ -3. The exclusion in this case is -3. However, if you choose 2y/2y+3, the exclusion would be y ≠ -3/2. That would mean no half-hearted y's allowed!
The correct rewriting of the algebraic fraction is y/(2)(y+3).
To explain how to get to this answer, let's break down the original expression:
4y(8y+24)^-1
First, we can simplify the expression within the parentheses (8y+24). This can be factored out to 8(y+3).
Now we have:
4y(8(y+3))^-1
Next, to simplify the fraction within the parentheses, we can divide each term by 8:
(4y/8)(1/(y+3))
Simplifying further, we have:
y/2(y+3)
So, the correct rewriting is y/(2)(y+3).
Now, let's look at the exclusion represented by the choice:
y ≠ -3
In this context, the exclusion means that we cannot let y be equal to -3. This is because if y is equal to -3, the denominator of the fraction (y+3) would become zero, which is undefined in algebra. Therefore, to avoid division by zero, we exclude y = -3 as a possible value in the original expression.