Problem

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

Solution

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 \(\boxed{\frac{9x-10}{x(x-5)}}\).

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Source: https://solvelyapp.com/problems/AiUjUo9sOm/

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