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Solve the following equation: 2/(2r – 1) – 5/3 = 1/(r + 2)

1. (-1, 5/2)
2. (1, -5/2)
3. (5/2, 1)
4. (2, 1)

QUICK ANSWER…

B

DETAILS…

Factorizing, we think of two numbers that on multiplying gives 10 (5 × 2), and on adding gives 3. The numbers are 5 and 2. Thus:

2r² + 3r – 5 = 0

2r² + 5r – 2r – 5 = 0

(2r² + 5r) –  1(2r + 5)= 0

r(2r + 5) –  1(2r + 5)= 0

(r – 1)(2r + 5) = 0

Thus, r – 1 = 0

Or 2r + 5 = 0

r = 1 or -5/2

Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is correct.
3. C is not correct.
4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

• Collecting like terms and resolving by LCM will lead to a quadratic equation.
• Solving the quadratic equation gives the answer.

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/ culled from 2021 JAMB-UTME MATHEMATICS question 1 /