(1500/x-1/2)-(1500/x)=100
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1500/(x - 1/2) - 1500/x = 100
⇒ 15 × 100 [ 1/(x -1/2) - 1/x ] = 100
⇒ 15 [ {x - (x -1/2)}/x(x -1/2) ] = 1
⇒ 15 [ 1/2/(x² - x/2) ] = 1
⇒ 15 [1/(2x² - x) ] = 1
⇒ 15 = 2x² - x
⇒2x² - x - 15 = 0
⇒2x² - 6x + 5x - 15 = 0
⇒2x(x - 3) + 5(x - 3) = 0
⇒(2x + 5)(x - 3) = 0
Hence, x = 3 and -5/2
⇒ 15 × 100 [ 1/(x -1/2) - 1/x ] = 100
⇒ 15 [ {x - (x -1/2)}/x(x -1/2) ] = 1
⇒ 15 [ 1/2/(x² - x/2) ] = 1
⇒ 15 [1/(2x² - x) ] = 1
⇒ 15 = 2x² - x
⇒2x² - x - 15 = 0
⇒2x² - 6x + 5x - 15 = 0
⇒2x(x - 3) + 5(x - 3) = 0
⇒(2x + 5)(x - 3) = 0
Hence, x = 3 and -5/2
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