How do you solve #(3x)/(x+1)=12/(x^2-1)+2#?

Question

Eva Abramson · Accepted Answer

Solution: #x=5 , x= -2#

# (3x)/(x+1)= 12/(x^2-1) +2# or

# (3x)/(x+1) -12/(x^2-1) = 2# Multiplying by #(x^2-1)# on both

sides we get # 3x(x-1) -12 = 2 (x^2-1) # or

# 3x^2-3x -12 = 2x^2-2 # or

# x^2-3x = 10 or x^2 -3x +9/4 = 10 +9/4 ; (9/4)# is added

to create a square L.H.S. on both sides.

# (x-3/2)^2 = 49/4 or x-3/2 = +- sqrt (49/4)# or

#x-3/2 = +- 7/2 :. x =3/2 +- 7/2 or x = 1/2( 3+-7) :.#

#x=5 , x= -2# . Solution: #x=5 , x= -2# [Ans]

Jace Anderson · Answer

undefined To solve the equation (3x)/(x+1) = 12/(x^2-1) + 2, we can follow these steps:

1. Start by multiplying both sides of the equation by (x+1) and (x^2-1) to eliminate the denominators.
2. Simplify the equation by distributing and combining like terms.
3. Rearrange the equation to bring all the terms to one side and set it equal to zero.
4. Factor the resulting quadratic equation, if possible.
5. Solve for x by setting each factor equal to zero and solving for x.
6. Check the solutions by substituting them back into the original equation to ensure they satisfy the equation.

By following these steps, you can find the solution(s) to the given equation.