Find the solution for the rational equation:

Answer:

To solve the equation , let’s first eliminate the fractions by finding a common denominator, which will be .

Multiplying through by the common denominator, we get:

This simplifies to:

Combining like terms gives:

Rearranging everything to one side results in:

Next, we can solve this quadratic using the quadratic formula, , where .

Calculating the discriminant:

Now applying the quadratic formula:

This gives us two possible solutions:

However, we must check for extraneous solutions by substituting back into the original equation and noting that makes the denominator of undefined.

Thus, the final solution is .