b. $\frac{\frac{2 - x - h}{1 + x + h} - \frac{2 - x}{1 + x}}{h}$

Question

Accepted Answer

# Explanation:
## Step1: Simplify the numerator
First, we simplify the numerator $\frac{2 - x - h}{1 + x + h}-\frac{2 - x}{1 + x}$. Find a common denominator $(1 + x + h)(1 + x)$:
$$
\begin{align*}
&\frac{(2 - x - h)(1 + x)-(2 - x)(1 + x + h)}{(1 + x + h)(1 + x)}\
=&\frac{(2(1 + x)-x(1 + x)-h(1 + x))-(2(1 + x + h)-x(1 + x + h))}{(1 + x + h)(1 + x)}\
=&\frac{2 + 2x - x - x^{2}-h - hx - 2 - 2x - 2h + x + x^{2}+hx}{(1 + x + h)(1 + x)}\
=&\frac{(2 - 2)+(2x - x - 2x + x)+(-x^{2}+x^{2})+(-h - 2h)+(-hx + hx)}{(1 + x + h)(1 + x)}\
=&\frac{-3h}{(1 + x + h)(1 + x)}
\end{align*}
$$

## Step2: Divide by $h$
Now, we have the original expression as $\frac{\frac{-3h}{(1 + x + h)(1 + x)}}{h}$. Dividing by $h$ is the same as multiplying by $\frac{1}{h}$:
$$
\frac{-3h}{(1 + x + h)(1 + x)}\times\frac{1}{h}=\frac{-3}{(1 + x + h)(1 + x)}
$$

# Answer:
$\frac{-3}{(1 + x)(1 + x + h)}$

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QUESTION IMAGE

Question

Explanation:

Step1: Simplify the numerator

Step2: Divide by \(h\)

Answer: