Question

M²+5m m⁴+125m ----------- : ------------------- =? 16m²-1 16m²-8m+1

Answer 1

$\frac{m(m+5)}{(4m-1)(4m+1)}* \frac{(4m-1)^{2}}{m(m^{3}+125)} =\frac{(m+5)(4m-1)}{(4m+1)(m+5)(m^{2}-5m+25)}= \frac{4m-1}{(4m+1)(m^{2}-5m+25)}$

Answer 2

To simplify the given expression:

M² + 5m

m⁴ + 125m

Divided by:

16m² - 1

16m² - 8m + 1

First, let's simplify the numerator and denominator separately.

Numerator: M² + 5m

Denominator: m⁴ + 125m

To simplify the numerator, we can factor out an 'm' from both terms:

m(M + 5)

To simplify the denominator, we notice that both terms have a common factor of 'm,' so we can factor it out:

m(m³ + 125)

Now, let's simplify the expression:

m(M + 5)

m(m³ + 125)

We can cancel out the common 'm' terms:

(M + 5)

m³ + 125

Now, let's simplify the second fraction:

16m² - 1

16m² - 8m + 1

This expression doesn't factor easily, so we'll leave it as it is.

The simplified expression is:

(M + 5)

m³ + 125

(16m² - 1)

(16m² - 8m + 1)

Please note that if you have specific values for 'M' and 'm,' you can substitute them into the expression to obtain a numerical result.