Solve : 2\((\frac{2x-1}{x+3})\) - 3\((\frac{x+3}{2x-1})\)= 5, x ≠

1.	Solve : 2\((\frac{2x-1}{x+3})\) - 3\((\frac{x+3}{2x-1})\)= 5, x ≠ - 3,\(\frac{1}{2}\).
Answer» 2((2x-1)/(x+3)) - 3((x+3)/(2x-1)) = 5, x ≠ - 3,1/2 ⇒ \(\frac{2(2x-1)^2-3(x+3)^2}{(x+3)(2x-1)}\) = 5 ⇒ 2(4x² − 4x + 1) − 3(x² + 6x + 9) = 5(x + 3)(2x − 1) ⇒ 8x² − 3x² − 8x − 18x + 2 − 27 = 10x² + 25x − 15 ⇒ 5x² − 26x − 25 = 10x² + 25x − 15 ⇒ 10x² − 5x² + 25x + 26x − 15 + 25 = 0 ⇒ 5x² + 51x + 10 = 0 ⇒ 5x² + x + 50x + 10 = 0 ⇒ 5x(5x + 1) + 10(5x + 1) = 0 ⇒ 5(x + 10)(5x + 1) = 0 ⇒ x + 10 = 0 or 5x + 1 = 0 ⇒ x = −10 or x = \(\frac{-1}{5}\). Hence, The solutions of given equation are x = \(\frac{-1}{5}\),-10.

Solve : 2\((\frac{2x-1}{x+3})\) - 3\((\frac{x+3}{2x-1})\)= 5, x ≠ - 3,\(\frac{1}{2}\).

Answer»

2((2x-1)/(x+3)) - 3((x+3)/(2x-1)) = 5, x ≠ - 3,1/2

⇒ \(\frac{2(2x-1)^2-3(x+3)^2}{(x+3)(2x-1)}\) = 5

⇒ 2(4x² − 4x + 1) − 3(x² + 6x + 9) = 5(x + 3)(2x − 1)

⇒ 8x² − 3x² − 8x − 18x + 2 − 27 = 10x² + 25x − 15

⇒ 5x² − 26x − 25 = 10x² + 25x − 15

⇒ 10x² − 5x² + 25x + 26x − 15 + 25 = 0

⇒ 5x² + 51x + 10 = 0

⇒ 5x² + x + 50x + 10 = 0

⇒ 5x(5x + 1) + 10(5x + 1) = 0

⇒ 5(x + 10)(5x + 1) = 0

⇒ x + 10 = 0 or 5x + 1 = 0

⇒ x = −10 or x = \(\frac{-1}{5}\).

Hence,

The solutions of given equation are x = \(\frac{-1}{5}\),-10.

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