Question

Solve
2(2x-1/x+3) - 3(x+3/2x-1) = 5,x ≠-3, ½​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

Answer

On putting $\sf \dfrac{2x - 1}{x + 3} = y$, the givrn equation becomes

$\sf \dashrightarrow 2y - \dfrac{3}{y} = 5$

$\sf \dashrightarrow {2y}^{2} - 3 = 5y$

$\sf \dashrightarrow {2y}^{2} - 5y - 3 = 0$

$\sf \dashrightarrow {2y}^{2} - 6y + y - 3 = 0$

$\sf \dashrightarrow 2y (y - 3) + (y - 3) = 0$

$\sf \dashrightarrow (y - 3) (2y + 1) = 0$

$\sf \dashrightarrow y - 3 =0 \: \: or \: \: 2y + 1 = 0$

$\sf \dashrightarrow y = 3 \: \: or \: \: y = \dfrac{-1}{2}$

Case 1 :-

$\sf \dashrightarrow y = 3$

$\sf \dashrightarrow \dfrac{2x - 1}{x + 3} = 3$

Cross multiply them.

$\sf \dashrightarrow 2x - 1 = 3 (x + 3)$

Multiply 3 with both numbers on RHS.

$\sf \dashrightarrow 2x - 1 = 3x + 9$

$\sf \dashrightarrow x = - 10$

Case 2 :-

$\sf \dashrightarrow y = \dfrac{-1}{2}$

$\sf \dashrightarrow \dfrac{2x - 1}{x + 3} = \dfrac{-1}{2}$

Cross multiply them.

$\sf \dashrightarrow 2 (2x - 1) = - (x + 3)$

Multiply 2 with both numbers on LHS.

$\sf \dashrightarrow 5x = - 1$

$\sf \dashrightarrow x = \dfrac{-1}{5}$

Thus, - 10 and $\sf \dfrac{-1}{5}$ are the roots of the given equation.