Question

A student solves the following equation and determines that the solution is −2. Is the student correct? Explain.

Answer 1

Answer:

No, the student did not check the solution to the derived equation in the original equation.

No, a possible solution is a = –2, but it does not check in the original equation because it makes two of the denominators equal to zero.

No, a = –2 is an extraneous solution, and there is no solution to the original rational equation.

Step-by-step explanation:

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Answer 2

Answer:

For this case, we have the following equation (according to the comments):

First, we factor the quadratic expression in the denominator:

Then, we multiply both sides of the equation by (a-2) (a + 2):

Later, canceling similar terms we have:

We do distributive property on the left side of the equation:

By grouping variables and constant terms we have:

Rewriting we have:

Finally, by clearing "a" we have:

Note: the value of a is a extraneous solution because it makes the denominator of the original equation equal to zero.

Answer:

the student correct, but the value of a= -2 is an extraneous solution