The expression [tex]\frac{m^{2}-16\cdot n^{2}}{\frac{3\cdot m + 12\cdot n}{m\cdot n} }[/tex] is equal to [tex]\frac{m^{2}\cdot n}{3} -\frac{4\cdot m\cdot n^{2}}{3}[/tex].
How to simplify a composite algebraic expression
In this question we must use properties of real algebra to simplify a given expression as most as possible. We proceed to show each step with respective reason.
- [tex]\frac{m^{2}-16\cdot n^{2}}{\frac{3\cdot m + 12\cdot n}{m\cdot n} }[/tex] Given
- [tex]\frac{m\cdot n \cdot (m^{2}-16\cdot n^{2})}{3\cdot m + 12\cdot n}[/tex] [tex]\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{c\cdot b}[/tex]
- [tex]\frac{m\cdot n \cdot (m-4\cdot n)\cdot (m+4\cdot n)}{3\cdot (m+4\cdot n)}[/tex] Distributive property/[tex]a^{2}-b^{2} = (a +b)\cdot (a-b)[/tex]
- [tex]\frac{m\cdot n \cdot (m-4\cdot n)}{3}[/tex] Existence of the multiplicative inverse/Modulative property
- [tex]\frac{m^{2}\cdot n}{3} -\frac{4\cdot m\cdot n^{2}}{3}[/tex] Distributive property/[tex]x^a\cdot x^{b} = x^{a+b}[/tex]/Result
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