Rational Equation
×-6/ײ-4x-12 + 2/x+2 = 1/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
Answers
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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Answer:
Thank you sa sagot:)
Step-by-step explanation:
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