Simplify \(\frac{2}{2 + x} + \frac{2}{2 - x}\)
Question 1 Report
Simplify \(\frac{2}{2 + x} + \frac{2}{2 - x}\)
Answer Details
To simplify the expression, we need to find a common denominator first. The denominators are \((2+x)\) and \((2-x)\), whose product is \((2+x)(2-x)=4-x^2\). So, we can write:
$$
\frac{2}{2 + x} + \frac{2}{2 - x} = \frac{2(2-x)}{(2+x)(2-x)} + \frac{2(2+x)}{(2+x)(2-x)} = \frac{4 - 2x + 4 + 2x}{4 - x^2} = \frac{8}{4 - x^2}
$$
Therefore, the simplified expression is \(\frac{8}{4 - x^2}\), which is option (B).
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