Question

How do you solve `\frac { 1} { x } - \frac { x + 7} { x ^ { 2} + 2x } = \frac { 4} { x }`?

Answer 1

x = -13/4

Explanation:

Given, `1/x-[x+7]/[x^2+2x]=4/x`

`rArr 1/x-[x+7]/[x(x+2)] = 4/x`

`rArr 1/x[1-{x+7}/{x+2}] =4/x` [Note: multiply both sides by x]

`rArr 1-[x+7]/[x+2] = 4` [Note: subtract (-1) from both sides]

`rArr 1-1-[x+7]/[x+2] = 4-1`

`rArr -[x+7]/[x+2] = 3` [Note: multiply both sides by (x+2)]

`rArr -[(x+7)(x+2)]/(x+2) = 3(x+2)`

`rArr -(x+7)= 3x+6`

`rArr -x-7 = 3x+6`

`rArr -x-3x = 6+7`

`rArr -4x = 13`

`rArr x = -13/4`