Question

How do you solve `2/( x +6) = 9/8 - 4/(x+6)`?

Answer 1

`x=-2/3`

Explanation:

`2/(x+6)=9/8-4/(x+6)`

`2/(x+6)-9/8+4/(x+6)=0`

`(2*8-9(x+6)+4*8)/(8(x+6))=0`

`(16-9x-54+32)/(8(x+6))=0`

`(-6-9x)/(8(x+6))=0`

`-6-9x=0 ^^ x+6 !=0`

`x=6/-9 ^^ x!=-6`

`x=-2/3`

Answer 2

x = -0.66666

Explanation:

2 / (x + 6) = 9 / 8 − 4 / (x + 6)
Transport − 4 / (x + 6) to the left hand side. We get
2 / (x + 6) + 4 / (x + 6) = 9 / 8
or 6 / (x + 6) = 9 / 8
Cross multiplying,
8 * 6 = 9 * (x + 6)
or 8 * 6 / 9 = x + 6
ie x = 8 * 6 / 9 - 6 = 5.333 - 6