The expression $\frac{m^{2}-16\cdot n^{2}}{\frac{3\cdot m + 12\cdot n}{m\cdot n} }$ is equal to $\frac{m^{2}\cdot n}{3} -\frac{4\cdot m\cdot n^{2}}{3}$ .

<h3>How to simplify a composite algebraic expression</h3>

In this question we must use properties of <em>real</em> algebra to simplify a given expression as most as possible. We proceed to show each step with respective reason.

$\frac{m^{2}-16\cdot n^{2}}{\frac{3\cdot m + 12\cdot n}{m\cdot n} }$ Given
$\frac{m\cdot n \cdot (m^{2}-16\cdot n^{2})}{3\cdot m + 12\cdot n}$ $\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{c\cdot b}$
$\frac{m\cdot n \cdot (m-4\cdot n)\cdot (m+4\cdot n)}{3\cdot (m+4\cdot n)}$ Distributive property/ $a^{2}-b^{2} = (a +b)\cdot (a-b)$
$\frac{m\cdot n \cdot (m-4\cdot n)}{3}$ Existence of the multiplicative inverse/Modulative property
$\frac{m^{2}\cdot n}{3} -\frac{4\cdot m\cdot n^{2}}{3}$ Distributive property/ $x^a\cdot x^{b} = x^{a+b}$ /Result

To learn more on algebraic expressions, we kindly invite to check this verified question: brainly.com/question/953809

7 0

3 years ago

Alejandro rounded the number 76.518 to 76.5. Jiro rounded the same number to 76.52. Who is correct? Explain your reasoning

sergeinik [125]

Alejandro is correct because you do not need to add another number to 76.518, as Jiro did, but you need to round it to the nearest tenth.

Glad I could help, and good luck!

4 0

3 years ago

Read 2 more answers

Please help I just need a <br> A

Tanzania [10]

Where is a????????????

3 0

4 years ago