Questions: multiple choice question Add or subtract the rational expression. 2/(g+10) + 2/(g^2-100) A. 2g-18/((g+10)(g-10)) B. 2g+22/((g+10)(g-10)) C. 4/(g^2+g-90) D. 4/((g+10)(g-10))

Solution Steps

To add the rational expressions \(\frac{2}{g+10}\) and \(\frac{2}{g^{2}-100}\), we first need to find a common denominator. Notice that \(g^2 - 100\) can be factored as \((g+10)(g-10)\). Thus, the common denominator for the two fractions is \((g+10)(g-10)\). We then rewrite each fraction with this common denominator and add them together.

To add the rational expressions \(\frac{2}{g+10}\) and \(\frac{2}{g^{2}-100}\), we first recognize that \(g^2 - 100\) can be factored as \((g+10)(g-10)\). Therefore, the common denominator for both fractions is \((g+10)(g-10)\).

We rewrite each fraction with the common denominator: \[ \frac{2}{g+10} = \frac{2(g-10)}{(g+10)(g-10)} \] \[ \frac{2}{g^{2}-100} = \frac{2}{(g+10)(g-10)} \]

Now we can add the two fractions: \[ \frac{2(g-10)}{(g+10)(g-10)} + \frac{2}{(g+10)(g-10)} = \frac{2(g-10) + 2}{(g+10)(g-10)} \]

Combining the numerators gives: \[ 2(g-10) + 2 = 2g - 20 + 2 = 2g - 18 \] Thus, the combined expression simplifies to: \[ \frac{2g - 18}{(g+10)(g-10)} \]

Final Answer