Answer:
[tex]\frac{1}{m-4}[/tex]
Step-by-step explanation:
[tex]\frac{\frac{4m-5}{m^4 -7m^3 +12m^2}}{\frac{4m-5}{m^3 -3m^2}}[/tex]
Factor the equation:
[tex]\frac{\frac{4m-5}{m^2(m^2 -7m+12)}}{\frac{4m-5}{m^2(m-3)}}[/tex]
[tex]\frac{\frac{4m-5}{m^2(m-3)(m-4)}}{\frac{4m-5}{m^2(m-3)}}[/tex]
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).
[tex]\frac{4m-5}{m^2(m-3)(m-4)}*\frac{m^2(m-3)}{4m-5}[/tex]
Simplify, take out common terms that are found on both the numerator and denominator
[tex]\frac{4m-5}{m^2(m-3)(m-4)}*\frac{m^2(m-3)}{4m-5}[/tex]
[tex]\frac{1}{m-4}[/tex]
