: 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?
the options are 10 30m^2 m^2 +5m or m^2( m+5)
10, with the restriction that m cannot be zero.
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.
To simplify the quotient (3m^2 + 15m) / (30 / m^2 + 5m) to its lowest terms, we need to follow these steps:
Step 1: Find the reciprocal of the denominator.
The reciprocal of (30 / m^2 + 5m) is (m^2 + 5m) / 30.
Step 2: Multiply the numerator by the reciprocal of the denominator.
(3m^2 + 15m) * (m^2 + 5m) / 30
Step 3: Simplify the numerator.
(3m^2 + 15m) * (m^2 + 5m) = 3m^4 + 15m^3 + 15m^3 + 75m^2
Step 4: Simplify the denominator.
30
Step 5: Simplify the expression further, if possible.
The numerator does not have any common factors that can be canceled out with the denominator. Therefore, the simplified expression is:
(3m^4 + 15m^3 + 15m^3 + 75m^2) / 30
Finally, the denominator of the resulting expression is 30.
To simplify the given expression and determine the denominator of the resulting expression, follow these steps:
Step 1: Simplify the numerator
The numerator is 3m^2 + 15m. It doesn't require any further simplification.
Step 2: Simplify the denominator
The denominator is (30/m^2) + 5m. To simplify it, we need to find a common denominator for the fraction and the term 5m.
Taking the reciprocal of the fraction, we get m^2/30. Now, the denominator is m^2/30 + 5m.
To find a common denominator, we multiply the first term by (m^2/m^2), which gives us m^2/30 + (5m)(m^2/m^2).
This simplifies to m^2/30 + 5m^3/ m^2.
Step 3: Divide the numerator by the simplified denominator
Now that we have the simplified numerator and denominator, we can divide the numerator by the denominator.
Dividing (3m^2 + 15m) by (m^2/30 + 5m^3/ m^2) is equivalent to multiplying the numerator by the reciprocal of the denominator.
(3m^2 + 15m) * (30/m^2 + m^2/ (5m^3))
Simplifying this expression further would involve expanding and combining like terms, which is not required to determine the denominator.
Step 4: Identify the denominator of the resulting expression
The denominator of the resulting expression is the denominator we obtained after simplifying the original expression.
From the previous step, the denominator is m^2 / 30 + 5m^3 / m^2.
Comparing the available options, we see that the correct answer is 10 since m^2 / 30 + 5m^3 / m^2 can be written as 10 when m ≠ 0.
Therefore, the correct option is 10.