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[tex]\frac{x+9}{5} - \frac{x+5}{5}= \frac{x+9-(x+5)}{5}=\frac{x+9-x-5}{5}=\boxed{\frac{4}{5}}[/tex]

Answer:

Given the statement: the quantity of x plus 9, all over 5 − the quantity of x plus 5, all over 5.

The quantity of x plus 9, all over 5 means [tex]\frac{x+9}{5}[/tex]

and

The quantity of x plus 5, all over 5 means [tex]\frac{x+5}{5}[/tex]

Then; we have;

[tex]\frac{x+9}{5}-\frac{x+5}{5}[/tex]

we can write this as ;

[tex]\frac{(x+9)-(x+5)}{5}[/tex]

⇒[tex]\frac{x+9-x-5}{5}[/tex]

Combine like terms;

⇒[tex]\frac{4}{5}[/tex]

therefore the simplified form of  the quantity of x plus 9, all over 5 − the quantity of x plus 5, all over 5 is, [tex]\frac{4}{5}[/tex]