Question

What is the solution to the equation 1/h-5+2/h+5=16/h^2-25 ?

Answer 1

(c) just took the test on edge

Answer 2

ANSWER

The solution to the equation is

`h = 7`
Step-by-step explanation

The equation given to us is

`(1)/(h - 5) + (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) * (1)/(h - 5) + (h + 5)(h - 5) * (2)/(h + 5) = \frac{16}{ {h}^(2) - 25} * (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.