Answer:
[tex]-4n+\frac{1}{3m}+4n-\frac{4}{5m}=-\frac{7}{15m}[/tex]
Step-by-step explanation:
Given the expression
[tex]-4n\:+\:\frac{1}{3m}\:+\:4n\:-\frac{4}{5m}[/tex]
Group like terms
[tex]-4n\:+\:\frac{1}{3m}\:+\:4n\:-\frac{4}{5m}=-4n+4n+\frac{1}{3m}-\frac{4}{5m}[/tex]
Adding similar elements: -4n + 4n = 0
[tex]=\frac{1}{3m}-\frac{4}{5m}[/tex]
L.C.M of 3m and 5n will be: 15m
so adjusting fractions based on the LCM
[tex]=\frac{5}{15m}-\frac{12}{15m}[/tex]
Since, the denominators are equal, combine the fractions: [tex]\frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{5-12}{15m}[/tex]
[tex]=\frac{-7}{15m}[/tex]
[tex]=-\frac{7}{15m}[/tex]
Therefore, we conclude that:
[tex]-4n+\frac{1}{3m}+4n-\frac{4}{5m}=-\frac{7}{15m}[/tex]
