ANSWER
The solution to the equation is
\(h = 7\)
EXPLANATION
The equation given to us is
\(\frac{1}{h - 5} + \frac{2}{h + 5} = \frac{16}{ {h}^{2} - 25}\)
The least common multiple of the denominators is,
\({h}^{2} - 25 = (h - 5)(h + 5)\)
We multiply through with the LCM to obtain,
\((h + 5)(h - 5) \times \frac{1}{h - 5} + (h + 5)(h - 5) \times \frac{2}{h + 5} = \frac{16}{ {h}^{2} - 25} \times (h + 5)(h - 5)\)
We cancel out common factors to obtain,
\(1(h + 5) + 2(h - 5) = 16\)
We expand the brackets to obtain,
\(h + 5 + 2h - 10 = 16\)
We group like terms to get,
\(h + 2h = 16 - 5 + 10\)
This simplifies to,
\(3h = 21\)
We now divide through by 3 to obtain,
\(h = 7\)
Therefore the solution is 7.
