Question

Help me please please i really need it​

Answer 1

Answers:

1. RAE
2. RAE
3. NOT
4. RAE
5. RAE

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Explanation:

A rational expression is when we divide one polynomial over another. The bottom polynomial cannot be zero. We can work with single variable polynomials or multivariable ones.

The first expression has us divide the multivariable polynomial $4a+8b$ over the constant polynomial $12$. Therefore, the expression $\frac{4a+8b}{12}$ is rational.

The same applies for the second expression $\frac{3c^8}{5d^4}$ because we're dividing the polynomial $3c^8$ over the polynomial $5d^4$ (both of which are considered monomials, but any monomial is a polynomial). So that's why $\frac{3c^8}{5d^4}$ is rational

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Unfortunately, the third expression is not rational. This is because the denominator is not a polynomial. The presence of the square root is the reason why.

You might be tempted to think the fourth expression isn't rational either, because we have another square root. But notice how $\sqrt{y^4} = \sqrt{ (y^2)^2} = y^2$ which means the square root goes away after simplifying. This shows that the fourth expression is rational. Always try to see if you can simplify any root terms to make them go away (if possible). We can't do that sort of trick for problem 3.

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The fifth expression is rational as well. The $\sqrt{z}$ terms cancel out when we divide, so those root terms go away. We're left with one polynomial divided by another.

To summarize, everything except problem 3 represents a rational expression.