Question

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

Answer 1

`(1)/(m-4)`

Explanation:

`((4m-5)/(m^4 -7m^3 +12m^2))/((4m-5)/(m^3 -3m^2))`

Factor the equation:

`((4m-5)/(m^2(m^2 -7m+12)))/((4m-5)/(m^2(m-3)))`

`((4m-5)/(m^2(m-3)(m-4)))/((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).

`(4m-5)/(m^2(m-3)(m-4))*(m^2(m-3))/(4m-5)`

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

`(4m-5)/(m^2(m-3)(m-4))*(m^2(m-3))/(4m-5)`

`(1)/(m-4)`