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

Feb 14, 2016

You must put on equivalent denominators.

Explanation:

The LCD (Least Common Denominator) is $\left(u - 1\right) \left(u + 1\right)$

$\frac{6 \left(u + 1\right) \left(u - 1\right)}{\left(u + 1\right) \left(u - 1\right)} + \frac{1 \left(u + 1\right)}{\left(u - 1\right) \left(u + 1\right)} = \frac{6 \left(u - 1\right)}{\left(u + 1\right) \left(u - 1\right)}$

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

$6 \left({u}^{2} - 1\right) + u + 1 = 6 u - 6$

$6 {u}^{2} - 6 + u + 1 - 6 u + 6 = 0$

$6 {u}^{2} - 5 u + 1 = 0$

Solve by factoring:

$6 {u}^{2} - 6 u + u + 1 = 0$

$6 u \left(u + 1\right) + 1 \left(u + 1\right) = 0$

$\left(6 u + 1\right) \left(u + 1\right) = 0$

$u = - \frac{1}{6} \mathmr{and} - 1$

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 $u = - \frac{1}{6}$.

Hopefully this helps!