How do you solve #[1/(x+4)+1/2]=[1/(x+4)]# and find any extraneous solutions?

Question

Savannah Anderson · Accepted Answer

No solutions.

By subtracting #1/(x+4)# from both sides, we get #1/2=0#. This is never true, so the equation has no solutions.

Nathan Axel · Answer

undefined To solve the equation [1/(x+4)+1/2]=[1/(x+4)] and find any extraneous solutions, we can follow these steps:

1. Start by multiplying both sides of the equation by the least common denominator (LCD), which is 2(x+4). This will help eliminate the denominators.

2. After multiplying, simplify the equation by distributing the LCD and combining like terms.

3. Next, isolate the variable x by moving all terms containing x to one side of the equation and simplifying further.

4. Solve the resulting equation for x.

5. Finally, check the solutions obtained by substituting them back into the original equation to identify any extraneous solutions. An extraneous solution is a solution that does not satisfy the original equation.

Please note that without the specific equation, it is not possible to provide the exact steps and solutions.