To simplify the expression \( \frac{8}{5} x - \frac{5}{16} \), we need to find a common denominator to combine the two fractions.
The denominators here are 5 and 16. The least common multiple (LCM) of 5 and 16 is 80.
Now, we rewrite each fraction with a denominator of 80:
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For \( \frac{8}{5} x \): \[ \frac{8}{5} x = \frac{8 \times 16}{5 \times 16} x = \frac{128}{80} x \]
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For \( \frac{5}{16} \): \[ \frac{5}{16} = \frac{5 \times 5}{16 \times 5} = \frac{25}{80} \]
Now we can rewrite the expression \( \frac{8}{5} x - \frac{5}{16} \) as: \[ \frac{128}{80} x - \frac{25}{80} \]
Since both terms now have a common denominator, we can combine them: \[ \frac{128x - 25}{80} \]
This is the expression in the simplest form. However, we also want to find if \( 128x - 25 \) can be simplified further. The numerator \( 128x - 25 \) does not have any common factors with 80, so we leave it as is.
The final result is: \[ \frac{128x - 25}{80} \]
Thus, the simplified expression is \( \frac{128x - 25}{80} \).
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