Questions: Subtract. Simplify, if possible. (4z-9)/(3z)-(3z-8)/(4z) (4z-9)/(3z)-(3z-8)/(4z)= (Simplify your answer. Use integers or fractions for any numbers in the expression.)

$Subtract. Simplify, if possible. (4z-9)/(3z)-(3z-8)/(4z) (4z-9)/(3z)-(3z-8)/(4z)= (Simplify your answer. Use integers or fractions for any numbers in the expression.)$

Transcript text: Subtract. Simplify, if possible. \[ \frac{4 z-9}{3 z}-\frac{3 z-8}{4 z} \] \[ \frac{4 z-9}{3 z}-\frac{3 z-8}{4 z}= \] $\square$ (Simplify your answer. Use integers or fractions for any numbers in the expression.)

Solution

Subtract and simplify the expression $ \frac{4z - 9}{3z} - \frac{3z - 8}{4z} $.

Find a common denominator.

The common denominator for $ 3z $ and $ 4z $ is $ 12z $.

Rewrite each fraction with the common denominator.

The first fraction becomes $ \frac{4z - 9}{3z} = \frac{4z - 9}{3z} \cdot \frac{4}{4} = \frac{16z - 36}{12z} $ and the second fraction becomes $ \frac{3z - 8}{4z} = \frac{3z - 8}{4z} \cdot \frac{3}{3} = \frac{9z - 24}{12z} $.

Perform the subtraction.

Now, we have $ \frac{16z - 36}{12z} - \frac{9z - 24}{12z} = \frac{(16z - 36) - (9z - 24)}{12z} = \frac{16z - 36 - 9z + 24}{12z} = \frac{7z - 12}{12z} $.

Simplify the expression.

The simplified expression is $ \frac{7}{12} - \frac{1}{z} $.

The final answer is $ \boxed{\frac{7}{12} - \frac{1}{z}} $.

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