Question

Please help and show all work so I can fully understand it, thanks.

Answer 1

Answer:

$\frac{1}{m-4}$

Step-by-step explanation:

$\frac{\frac{4m-5}{m^4 -7m^3 +12m^2}}{\frac{4m-5}{m^3 -3m^2}}$

Factor the equation:

$\frac{\frac{4m-5}{m^2(m^2 -7m+12)}}{\frac{4m-5}{m^2(m-3)}}$

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

Rewrite to suit the format of multiplying two fractions. Remember, dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second. A reciprocal of a fraction is when one switches the place of the numerator and the denominator, that is, the value on top (numerator), and the value on the bottom (denominator).

$\frac{4m-5}{m^2(m-3)(m-4)}*\frac{m^2(m-3)}{4m-5}$

Simplify, take out common terms that are found on both the numerator and denominator

$\frac{4m-5}{m^2(m-3)(m-4)}*\frac{m^2(m-3)}{4m-5}$

$\frac{1}{m-4}$