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

1 Answer
Feb 14, 2016

Answer:

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!