The equivalent expression of [tex]\frac{5}{m}-\frac{m+8}{m^{2} - 4m}[/tex] is [tex]\frac{4(m-7)}{m(m-4)}[/tex]
How to simplify an expression?
The expression can be simplified as follows:
[tex]\frac{5}{m}-\frac{m+8}{m^{2} - 4m}[/tex]
[tex]\frac{5}{m}-\frac{m+8}{m^{2} - 4m} = \frac{5(m^{2} - 4m)-m(m+8)}{m(m^{2} - 4m)}[/tex]
Therefore,
[tex]\frac{5(m^{2} - 4m)-m(m+8)}{m(m^{2} - 4m)}=\frac{5m^{2} - 20m-m^{2}-8m}{m(m^{2}-4m )}[/tex]
Simplifying further,
[tex]\frac{5m^{2} - 20m-m^{2}-8m}{m(m^{2}-4m )}=\frac{5m^{2}-m^{2}-20m-8m }{m(m^{2}-4m )}[/tex]
[tex]\frac{5m^{2}-m^{2}-20m-8m }{m(m^{2}-4m )} = \frac{4m^{2} -28m}{m(m^{2}-4m)}[/tex]
[tex]\frac{4m^{2} -28m}{m(m^{2}-4m)} = \frac{4m(m-7)}{m^{2}(m-4) }[/tex]
Finally,
[tex]\frac{4m(m-7)}{m^{2}(m-4) }=\frac{4(m-7)}{m(m-4)}[/tex]
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