Question

Which expression is equivalent to the expression below? startfraction m 3 over m squared minus 16 endfraction divided by startfraction m squared minus 9 over m 4 endfraction startfraction 1 over (m 4) (m 3) endfraction startfraction 1 over (m minus 4) (m minus 3) endfraction startfraction m minus 4 over m minus 3 endfraction startfraction m 3 over m 4 endfraction

Answer 1

The equivalent expression of the product expression $\frac{m^3}{m^2 - 16} \div \frac{m^2 - 9}{m^4}$ is $\frac{m^7}{(m - 4)(m + 4)(m - 3)(m + 4)}$

How to determine the equivalent expression?

The expression is given as:

$\frac{m^3}{m^2 - 16} \div \frac{m^2 - 9}{m^4}$

Rewrite the expression as a product

$\frac{m^3}{m^2 - 16} * \frac{m^4}{m^2 - 9}$

Evaluate the product

$\frac{m^7}{(m^2 - 16)(m^2 - 9)}$

Rewrite the denominator as a difference of two squares

$\frac{m^7}{(m - 4)(m + 4)(m - 3)(m + 4)}$

Hence, the equivalent expression of the product expression $\frac{m^3}{m^2 - 16} \div \frac{m^2 - 9}{m^4}$ is $\frac{m^7}{(m - 4)(m + 4)(m - 3)(m + 4)}$

Read more about equivalent expressions at:

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