Question

For the rational equation, x^2+5x+6/x+3=3 , what is a valid value of x?.

Answer 1

The answer for this question is 1

Answer 2

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.

$\frac{x^{2}+5x+6}{(x+3)}=3$

By cross multiplication

$x^{2}+5x+6=3(x+3)$

We factorize left hand side (L.H.S.) of the equation first.

$x^{2}+5x+6=x^{2}+3x+2x+6$

         = $x(x+3)+2(x+3)$

         = $(x+2)(x+3)$

Now factorized form of the eqation is

$(x+2)(x+3)=3(x+3)$

$(x+2)(x+3)-3(x+3)=0$

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

x+3= 0 ⇒ x = -3

x - 1 = 0 ⇒  x = 1

Therefore, x= -3 and x = 1 are the values.