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# Which statement best reflects the solution(s) of the equation?

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Which statement best reflects the solution(s) of the equation?

x / x−1 − 1 / x−2   =   2x−5 / x^2−3x+2

A - There are two solutions: x = 2 and x = 3.

B- There is only one solution: x = 3.
The solution x = 2 is an extraneous solution.

C -There is only one solution: x = 3.
The solution x = 1 is an extraneous solution.

D - There is only one solution: x = 4.
The solution x = 1 is an extraneous solution.

Oct 19, 2018

#1
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Solve for x:
x/(x - 1) - 1/(x - 2) = (2 x - 5)/(x^2 - 3 x + 2)

Multiply both sides by x^2 - 3 x + 2:
1 - x + x (x - 2) = 2 x - 5

Expand out terms of the left hand side:
x^2 - 3 x + 1 = 2 x - 5

Subtract 2 x - 5 from both sides:
x^2 - 5 x + 6 = 0

The left hand side factors into a product with two terms:
(x - 3) (x - 2) = 0

Split into two equations:
x - 3 = 0 or x - 2 = 0

x = 3 or x - 2 = 0

x = 3 or x = 2

x/(x - 1) - 1/(x - 2) ⇒ 2/(2 - 1) - 1/(2 - 2) = ∞^~
(2 x - 5)/(x^2 - 3 x + 2) ⇒ (2 2 - 5)/(2 - 3 2 + 2^2) = ∞^~:
So this solution is incorrect

x/(x - 1) - 1/(x - 2) ⇒ 3/(3 - 1) - 1/(3 - 2) = 1/2
(2 x - 5)/(x^2 - 3 x + 2) ⇒ (2 3 - 5)/(2 - 3 3 + 3^2) = 1/2:
So this solution is correct

The solution is: x = 3      The answer is "B"

Oct 19, 2018

#1
+1

Solve for x:
x/(x - 1) - 1/(x - 2) = (2 x - 5)/(x^2 - 3 x + 2)

Multiply both sides by x^2 - 3 x + 2:
1 - x + x (x - 2) = 2 x - 5

Expand out terms of the left hand side:
x^2 - 3 x + 1 = 2 x - 5

Subtract 2 x - 5 from both sides:
x^2 - 5 x + 6 = 0

The left hand side factors into a product with two terms:
(x - 3) (x - 2) = 0

Split into two equations:
x - 3 = 0 or x - 2 = 0

x = 3 or x - 2 = 0

x = 3 or x = 2

x/(x - 1) - 1/(x - 2) ⇒ 2/(2 - 1) - 1/(2 - 2) = ∞^~
(2 x - 5)/(x^2 - 3 x + 2) ⇒ (2 2 - 5)/(2 - 3 2 + 2^2) = ∞^~:
So this solution is incorrect

x/(x - 1) - 1/(x - 2) ⇒ 3/(3 - 1) - 1/(3 - 2) = 1/2
(2 x - 5)/(x^2 - 3 x + 2) ⇒ (2 3 - 5)/(2 - 3 3 + 3^2) = 1/2:
So this solution is correct

The solution is: x = 3      The answer is "B"

Guest Oct 19, 2018