: if the quotient 3m^2 +15m / m^2 divided by 30/ m^2 + 5m is simplified to lowest terms, which of the following is the denominator of the resulting expression?

Question

the options are 10 30m^2 m^2 +5m or m^2( m+5)

10, with the restriction that m cannot be zero.

Answer 1

If we simplify the given expression, we first need to express the division as multiplication. The expression becomes:

(3m^2 +15m) / (m^2) * (m^2 + 5m) / 30

Now we can simplify further by factoring:

(3m(m + 5)) / (m^2) * (m^2 + 5m) / 30

We can cancel the (m^2 + 5m) term:

= (3m) * 1 / 30

Now let's simplify by factoring out a 3 from both the numerator and the denominator:

= m * 1 / 10

So the final answer is that the denominator is 10, with the restriction that m cannot be zero.