Question

Simplify 16m^2/m^2+5/4m/3m^2+15

Answer 1

Answer:

12m

Step-by-step explanation:

We are given the following expression where a fraction is divided by another fraction:

$\frac{\frac{16m^2}{m^2+5} }{\frac{4m}{3m^2+15} }$

To change this division into multiplication, we will take reciprocal of the fraction in the denominator and then solve:

$\frac { 1 6 m ^ 2 } { m^2+5} } \times \frac{3m^2+15}{4m}$

Factorizing the terms to simplify:

$\frac { 4 m ( 4m ) } { m ^ 2 + 5 } \times \frac { 3 ( m ^ 2 + 5 ) } { 4 m }$

Cancelling the like terms to get:

12m

Answer 2

Answer: $12m$

Step-by-step explanation:

Given the expression $\frac{\frac{16m^2}{m+5}}{\frac{4m}{3m^2+15}}$, we can rewrite it in this form:

$(\frac{16m^2}{m+5})(\frac{3m^2+15}{4m})$

Now we must multiply the numerator of the first fraction by the numerator of the second fraction and   the denominator of the first fraction by the denominator of the second fraction:

 $=\frac{(16m^2)(3m^2+15)}{(m^2+5)(4m)}}$

According to the Quotient of powers property:

$\frac{a^m}{a^n}=a^{(m-n)}$

And the Product of powers property states that:

$(a^m)(a^n)=a^{(m+n)}$

Then, simplifying, we get:

$=\frac{3(m^2+5)(4m)(4m)}{(m^2+5)(4m)}}\\\\=3(4m)\\\\=12m$