Answer :
Answer:
x= -3 and x = 1 are the values.
Step-by-step explanation:
For the rational equation given we have to find the value of x.
[tex]\frac{x^{2}+5x+6}{(x+3)}=3[/tex]
By cross multiplication
[tex]x^{2}+5x+6=3(x+3)[/tex]
We factorize left hand side (L.H.S.) of the equation first.
[tex]x^{2}+5x+6=x^{2}+3x+2x+6[/tex]
= [tex]x(x+3)+2(x+3)[/tex]
= [tex](x+2)(x+3)[/tex]
Now factorized form of the eqation is
[tex](x+2)(x+3)=3(x+3)[/tex]
[tex](x+2)(x+3)-3(x+3)=0[/tex]
[tex](x+3)(x-1)=0[/tex]
x+3= 0 ⇒ x = -3
x - 1 = 0 ⇒ x = 1
Therefore, x= -3 and x = 1 are the values.