Chapter 7.4, Problem 35WE

To determine

To solve: the expression as mentioned in the problem.

Answer to Problem 35WE

The solution exist and it is $x=-\frac{14}{3}$.

Explanation of Solution

Given information:

The expression is $\frac{3}{x-4}+\frac{2}{x^2-16}=0$.

Formula used:

We will use cross multiplication method.

We will use L.C.M of the denominator.

Calculation:

Consider the expression $\frac{3}{x-4}+\frac{2}{x^2-16}=0$.

Here variable is $x$ in the mentioned expression above.

Recall that we will use L.C.M of the denominator.

Therefore the L.C.M of $\left(x-4,x^2-16\right)$ is $\left(x^2-16\right)$.

Therefore $\frac{3}{x-4}+\frac{2}{x^2-16}=0\Rightarrow \frac{3*\left(x+4\right)+2*1}{\left(x^2-16\right)}=0\Rightarrow \frac{3x+12+2}{\left(x^2-16\right)}=0$.

Recall that we will use cross multiplication method.

  $\frac{3x+14}{\left(x^2-16\right)}=0\Rightarrow 3x+14=0\Rightarrow x=\frac{-14}{3}$.

Therefore the value of the expression has a solution $x=-\frac{14}{3}$.