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

Question

Eva Adamson · Accepted Answer

You must make all the fractions equivalent by putting them on an equivalent denominator.

(x + 2)(x - 2) is the LCD (Least Common Denominator). #(x(x - 2))/((x + 2)(x - 2)) - (2(x + 2))/((x - 2)(x + 2)) = (x^2 + 4)/((x - 2)(x + 2))# The denominators can now be eliminated. #x^2 - 2x - 2x - 4 = x^2 + 4# #x^2 - x^2 - 4x - 8 = 0# #-4x = 8# #x = -2# The equation has no solution since x= -2 sets some of the denominators to 0. Hopefully, this is useful!

Genesis Allen · Answer

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

1. Start by finding a common denominator for all the fractions involved. In this case, the common denominator is (x+2)(x-2).

2. Multiply each term by the common denominator to eliminate the fractions. This gives us:
   x(x-2) - 2(x+2) = (x^2+4)

3. Expand and simplify the equation:
   x^2 - 2x - 2x - 4 = x^2 + 4

4. Combine like terms on both sides of the equation:
   x^2 - 4x - 4 = x^2 + 4

5. Subtract x^2 from both sides to eliminate the x^2 terms:
   -4x - 4 = 4

6. Add 4 to both sides to isolate the x term:
   -4x = 8

7. Divide both sides by -4 to solve for x:
   x = -2

Therefore, the solution to the equation x/(x+2) - 2/(x-2) = (x^2+4)/(x^2-4) is x = -2.