`x/(x+1)=3/(x+1)` Solve the equation by cross multiplying. Check for extraneous solutions.

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

cross multiply,

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

`x*x+x*1=3*x+3*1`

`x^2+x=3x+3`

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

Factorize,

`x(x+1)-3(x+1)=0`

`(x+1)(x-3)=0`

use zero product property,

`x+1=0` or `x-3=0`

`x=-1` or `x=3`

Now let's check the solutions by plugging them in the original equation,

For x=-1

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

`(-1)/0=3/0`

It's an extraneous solution, as it leads to division by zero.

For x=3,

`3/(3+1)=3/(3+1)`

`3/4=3/4`

It's true.

So, the solution of the equation is x=3

Notes