Question

What is the solution to the equation?A. h=11/3B.h=5C.h=21/2D. h=7

Answer 1

Answer:

D. h=7

Step-by-step explanation:

1               2            16

------ + ------------ = ----------

h-5        h+5          (h^2 -25)

1               2            16

------ + ------------ = ----------

h-5        h+5          (h-5)(h+5)

Since h^2 -25 factors in (h-5) (h+5)  ( it is the difference of squares)

We will multiply both sides by  (h-5) (h+5)  to clear the fractions

(h-5) (h+5)              2 (h-5) (h+5)            16 (h-5) (h+5)

------              + ------------                     = ----------

h-5                   h+5                                (h-5)(h+5)

Canceling like terms

 (h+5)              2 (h-5)             16

------              + ------------      = ----------

1                         1                          1

h+5 + 2(h-5) = 16

Distribute

h+5 + 2h -10 = 16

Combine like terms

3h-5=16

Add 5 to each side

3h-5+5 =16+5

3h =21

Divide each side by 3

3h/3 = 21/3

h = 7