Question

How do you solve rational equations `6 + 1/(u-1) = 6 / (u+1)`?

Answer 1

You must put on equivalent denominators.

Explanation:

The LCD (Least Common Denominator) is `(u - 1)(u + 1)`

`(6(u + 1)(u - 1))/((u + 1)(u - 1)) + (1(u + 1))/((u - 1)(u + 1)) = (6(u - 1))/((u + 1)(u - 1))`

We can now eliminate denominators, since all fractions are equivalent.

`6(u^2 - 1) + u + 1 = 6u - 6`

`6u^2 - 6 + u + 1 - 6u + 6 = 0`

`6u^2 - 5u + 1 = 0`

Solve by factoring:

`6u^2 - 6u + u + 1 = 0`

`6u(u + 1) + 1(u + 1) = 0`

`(6u + 1)(u + 1) = 0`

`u = -1/6 and -1`

However, we cannot except -1 as a solution because it is a non permissible value. Non-permissible values are numbers that can't be used in the denominators because they make the denominators equal to 0, and division by 0 is non defined. So, the solution is `u= -1/6`.

Hopefully this helps!