2. 11 Rational Equation x - 6 2 + x2 - 4x – 12 x+2 +N x26 x - 6 1. Find the Least Common Denominator (LCD). 2. Multiply both sides of the equation by its the LCD. 3. Apply the Distributive Property and then simplify. 4. Find all the possible values of x. x = 10 5. Check each value by substituting into original equation and reject any extraneous root/s

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Samuelallen0523go Samuelallen0523go · Answer 1

Answer: RHS = 1/(10 - 6) = 1/4

LHS = RHS = 1/4

Given : (x - 6 )/ (x² - 4x - 12) + 2/(x + 2) = 1/(x - 6)

To Find : Solve for x and verify

Solution:

(x - 6 )/ (x² - 4x - 12) + 2/(x + 2) = 1/(x - 6)

x² - 4x - 12 = (x - 6)(x + 2)

=(x - 6 )/ (x - 6)(x + 2) + 2/(x + 2) = 1/(x - 6)

Hence Denominator LCD = (x - 6)(x + 2) = x² - 4x - 12

Multiply both sides of the equation by its the LCD. (x - 6)(x + 2)

= (x - 6) + 2(x - 6) = x + 2

=> x - 6 + 2x - 12 = x + 2

=> 3x - 18 = x + 2

=> 2x = 20

=> x = 10

(x - 6 )/ (x² - 4x - 12) + 2/(x + 2) = 1/(x - 6)

Substitute x = 10

LHS = (10 - 6 )/ (10² - 4(10) - 12) + 2/(10 + 2)

= 4/(100 - 40 - 12) + 2/12

= 4/48 + 2/12

= 1/12 + 2/12

= 3/12

= 1/4

RHS = 1/(10 - 6) = 1/4

LHS = RHS = 1/4

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