How do you solve for x: #2/(x-3) - 3/(x+3) = 12/((x^2)-9) #?

Question

Eli Assouline · Accepted Answer

#2/(x-3)-3/(x+3)=12/(x^2-9)# #implies (2(x+3)-3(x-3))/((x+3)(x-3))=12/(x^2-9)# #implies (2x+6-3x+9)/cancel(x^2-9)=12/cancel(x^2-9)# #implies -x+15=12# #implies x=3# Verification: Put #x=3# #L.H.S=2/(x-3)-3/(x+3)=2/(3-3)-3/(3+3)=2/0-3/6# Here we can see #2/0#, in Mathematics, division by 0 is not allowed.
Hence, the root #x=3# is not a solution to the given equation.
Hence, no solution exists for the given equation.

Julia Adams · Answer

undefined To solve for x in the equation 2/(x-3) - 3/(x+3) = 12/((x^2)-9), we can follow these steps:

1. Find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is (x-3)(x+3).

2. Multiply each term by the common denominator to eliminate the fractions.

3. Simplify the equation by distributing and combining like terms.

4. Rearrange the equation to isolate the variable x.

5. Solve for x by factoring or using the quadratic formula if necessary.

The final solution(s) for x will depend on the specific values obtained during the solving process.