Question

What is the solution to the equation 

Answer 1

Multiply the equation by h²-25.
   1(h +5) + 2(h -5) = 16
   3h -5 = 16 . . . . . . . . . . collect terms
   3h = 21 . . . . . . . . . . . . add 5
   h = 7 . . . . . . . . . . . . . . divide by 3

The solution is h = 7.

_____
Check
1/(7-5) + 2/(7+5) = 16/(7²-25)
1/2 + 2/12 = 16/24
3/6 + 1/6 = 4/6 . . . . . yes, the answer satisfies the equation.

Answer 2

Hi there!

$\dfrac {1}{h - 5} + \dfrac {2}{h + 5} = \dfrac {16}{h^{2} - 25}$

$\dfrac {h + 5 + 2(h - 5)}{h^{2} - 25} = \dfrac {16}{h^{2} - 25}$

Multiply h² - 25 both sides of th' Eqn. :-

$\dfrac {h + 5 + 2(h - 5)}{h^{2} - 25} × h^{2} - 25 = \dfrac {16}{h^{2} - 25}$ × $h^{2} - 25$

h + 5 + 2h - 10 = 16

3h - 5 = 16

3h = 16 + 5

3h = 21

h = $\dfrac{21}{3}$ = 7

Hence, h = 7

~ Hope it helps!