\frac{\frac{1-\left(z-h\right)}{2\left(z-h\right)}-\frac{1-z}{2z}}{h}

asked by guest
on Jan 08, 2025 at 8:51 am



You asked:

Evaluate the expression: \(\frac{\frac{1 - \left(z - h\right)}{2 \left(z - h\right)} - \frac{1 - z}{2 z}}{h}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\frac{1 - \left(z - h\right)}{2 \left(z - h\right)} - \frac{1 - z}{2 z}}{h} = \frac{\frac{h - z + 1}{- 2 h + 2 z} - \frac{1 - z}{2 z}}{h} \)

Expanded

\[\frac{\frac{1 - \left(z - h\right)}{2 \left(z - h\right)} - \frac{1 - z}{2 z}}{h} = - \frac{z}{- 2 h^{2} + 2 h z} + \frac{1}{- 2 h^{2} + 2 h z} + \frac{1}{- 2 h + 2 z} + \frac{1}{2 h} - \frac{1}{2 h z}\]

Factored

\[\frac{\frac{1 - \left(z - h\right)}{2 \left(z - h\right)} - \frac{1 - z}{2 z}}{h} = - \frac{1}{2 z \left(h - z\right)}\]

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