Add.
\[
\frac{2}{x}+\frac{7}{x-5}
\]
$\frac{2}{x}+\frac{7}{x-5}=\square($ Simplify your answer.)

Answer

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Answer

The simplified form of the given expression is $\boxed{\frac{9x-10}{x(x-5)}}$.

Steps

Step 1 ：The given expression is $\frac{2}{x}+\frac{7}{x-5}$.

Step 2 ：The common denominator of $\frac{2}{x}$ and $\frac{7}{x-5}$ is $x(x-5)$.

Step 3 ：We need to convert each fraction to have this common denominator.

Step 4 ：The first fraction becomes $\frac{2(x-5)}{x(x-5)}$.

Step 5 ：The second fraction becomes $\frac{7x}{x(x-5)}$.

Step 6 ：Adding these two fractions together, we get $\frac{2x-10+7x}{x(x-5)}$.

Step 7 ：Simplifying the numerator, we get $\frac{9x-10}{x(x-5)}$.

Step 8 ：The simplified form of the given expression is $\boxed{\frac{9x-10}{x(x-5)}}$.