Answer:
h=7
Step-by-step explanation:
We want to solve the equation:
[tex]\frac{1}{h-5}+\frac{2}{h+5}=\frac{16}{h^2-25}[/tex]
We multiply through by the LCM: [tex]h^2-25=(h+5)(h-5)[/tex]
[tex](h^2-25*\frac{1}{h-5}+(h^2-25)*\frac{2}{h+5}=\frac{16}{h^2-25} \times(h^2-25)[/tex]
Simplify to get:
[tex]h+5+2(h-5)=16[/tex]
We expand to get:
[tex]h+5+2h-10=16[/tex]
[tex]h+2h=16+10-5[/tex][tex]3h=21[/tex]
h=7
