- 2 +1 +2 3x - 3 *+2 x + 1)(x+2) 9. (x - 3 )/(x + 2) + (3x - 3)/((x + 1)(x + 2) = (x)/(x + 1) - (x - 2)/(x + 2) ​

Question

-

2
+1 +2
3x - 3
*+2 x + 1)(x+2)
9.

`(x - 3 )/(x + 2) + (3x - 3)/((x + 1)(x + 2) = (x)/(x + 1) - (x - 2)/(x + 2)`
​

Answer 1

Given:

The equation is:

`(x-3)/(x+2)+(3x-3)/((x+1)(x+2))=(x)/(x+1)-(x-2)/(x+2)`

To find:

The solution for the given equation.

Solution:

We have,

`(x-3)/(x+2)+(3x-3)/((x+1)(x+2))=(x)/(x+1)-(x-2)/(x+2)`

Taking LCM on both sides, we get

`((x-3)(x+1)+3x-3)/((x+1)(x+2))=(x(x+2)-(x+1)(x-2))/((x+1)(x+2))`

`(x-3)(x+1)+3x-3=x(x+2)-(x+1)(x-2)`

`x^2+x-3x-3+3x-3=x^2+2x-(x^2-2x+x-2)`

`x^2+x-6=x^2+2x-x^2+2x-x+2`

On further simplification, we get

`x^2+x-6=3x+2`

`x^2+x-6-3x-2=0`

`x^2-2x-8=0`

Splitting the middle term, we get

`x^2-4x+2x-8=0`

`x(x-4)+2(x-4)=0`

`(x+2)(x-4)=0`

`x=-2,4`

But
`x\\eq -2` because for
`x=-2` the given equation is not defined.

Therefore, the only solution of the given equation is
`x=4`.