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`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 

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