Question

What is the solution to the equation?

A. h=11/3

B.h=5

C.h=21/2
D. h=7

Answer 1

D. h=7

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