Solve for x 4/(x-6)+12/(x+6)=144/(x^2-36)

Problem

4/(x−6)+12/(x+6)=144/(x^2−36)

Solution

1. Factor the denominator on the right side of the equation using the difference of squares formula.

x^2−36=(x−6)*(x+6)

2. Identify the least common denominator (LCD) for all terms in the equation.

LCD=(x−6)*(x+6)

3. Multiply every term in the equation by the LCD to eliminate the fractions.

(x−6)*(x+6)*(4/(x−6))+(x−6)*(x+6)*(12/(x+6))=(x−6)*(x+6)*(144/((x−6)*(x+6)))

4. Simplify the resulting linear equation by canceling common factors.

4*(x+6)+12*(x−6)=144

5. Distribute the constants into the parentheses.

4*x+24+12*x−72=144

6. Combine like terms on the left side of the equation.

16*x−48=144

7. Isolate the term containing x by adding 48 to both sides.

16*x=192

8. Solve for x by dividing both sides by 16.

x=12

9. Verify that the solution does not make any denominator in the original equation equal to zero.

12−6≠0

12+6≠0

Final Answer

4/(x−6)+12/(x+6)=144/(x^2−36)⇒x=12

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