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

Question

Abigail Allen · Accepted Answer

You must put on equivalent denominators.

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!

Julia Adams · Answer

undefined To solve the rational equation 6 + 1/(u-1) = 6 / (u+1), you can follow these steps:

1. Start by multiplying both sides of the equation by the least common denominator (LCD) of (u-1) and (u+1), which is (u-1)(u+1).

2. Distribute the LCD to each term in the equation.

3. Simplify the equation by canceling out common factors.

4. Solve for u by isolating the variable on one side of the equation.

5. Check your solution by substituting the value of u back into the original equation to ensure it satisfies the equation.

Please note that the solution may involve restrictions on the variable u, such as values that make the denominator zero.