How do you solve #4 / (x+1) + 3 / (x - 4) = 2 / (x +1)#?

Question

Julia Adams · Accepted Answer

#x=1#

Normally, the denominators would be cancelled by multiplying by the LCD; however, since two of the denominators are the same, combine them onto one side.

#4 / (x+1) + 3 / (x - 4) = 2 / (x +1)#

#color(red)(4 / (x+1) - 2 / (x +1)) = - 3 / (x - 4)#

#(2)/(x+1) = 3/-(x-4)" "larr# one fraction each side, cross-multiply

#3(x+1) = -2(x-4)#

#3x+3 =-2x+8#

#3x+2x = 8-3#

#5x = 5#

#x =1#

Eva Adamson · Answer

undefined To solve the equation 4 / (x+1) + 3 / (x - 4) = 2 / (x +1), we can follow these steps:

1. Start by multiplying every term in the equation by the common denominator, which is (x+1)(x-4). This will help eliminate the denominators.

2. After multiplying, simplify the equation by distributing and combining like terms.

3. Continue simplifying until you have a quadratic equation in standard form, ax^2 + bx + c = 0.

4. Solve the quadratic equation using factoring, completing the square, or the quadratic formula.

5. Check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

Please note that the solution may involve restrictions on the values of x, such as excluding any values that would make the denominators zero.