Answer:
x = √17 and x = -√17
Step-by-step explanation:
We have the equation:
To solve this we need to remove the denominators.
Then we can first multiply both sides by (x + 4) to get:
Now we can multiply both sides by (x + 3)
Now we can multiply both sides by (x^2 + 7*x + 12)
Now we need to solve this:
we will get
Then we get:
So now we only need to solve this.
We can see that the constant is 51.
Then one root will be a factor of 51.
The factors of -51 are:
-3 and -17
Let's try -3
p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0
Then x = -3 is one solution of the equation.
But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.
This means that we can take a factor (x + 3) out, so we can rewrite our equation as:
The other two solutions are when the other term is equal to zero.
Then the other two solutions are given by:
x = ±√17
And neither of these have problems in the denominators, so we can conclude that the solutions are:
x = √17 and x = -√17