For items 5-6:Refer to the rational equation below.
5/2x-4 + 2/x+3 = 3/x-2
5. To solve the equation, we multiply both sides by
A x-2
B. x+3
C. (x+2)(x-3)
D. (x-2)(x+3)
6. Which of the following will be the solution to the given rational equation?
A. 113
B. 311
C. -113
D.-311
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Rational Equation
To solve rational equations, find the least common denominator. Multiply both sides of the equation by the least common denominator. Apply the distributive property. Simplify the answer. Find all the possible value of x and reject extraneous root/s if there is any.
Answers:
5. D.
6. A.
Solutions:
5. Given:
+ 
= 
Find the least common denominator.
2x - 4 = 2(x - 2)
x + 3 = x + 3
x - 2 = x - 2
Therefore, the least common denominator is (x - 2)(x + 3). So, we will multiply both sides of the rational equation by D. (x - 2)(x + 3).
6. Given:
+ 
= 
Solve the equation:
find the least common denominator: 2(x - 2)(x + 3)
multiply both sides of the equation by the least common denominator:
2(x - 2)(x + 3)[
+ 
= 
]
5(x + 3) + 2(2x - 4) = 3(2x + 6)
5x + 15 + 4x - 8 = 6x + 18
5x + 4x - 6x = -15 + 8 +18
9x - 6x = -15 + 26
3x = 11
x =
How to solve rational equation: brainly.ph/question/6624603
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