solve for x ; 2(2x+3/x-3)-25(x-3/2x+3) = 5 - Maths - Quadratic Equations

Question

solve for x ; 2(2x+3/x-3)-25(x-3/2x+3) = 5

Ankush Jain · Accepted Answer

The given equation is $2 (\frac{2 x + 3}{x - 3}) - 25 (\frac{x - 3}{2 x + 3}) = 5$

$2 (\frac{2 x + 3}{x - 3}) - 25 (\frac{x - 3}{2 x + 3}) = 5 \Rightarrow \frac{2 (2 x + 3)^{2} - 25 (x - 3)^{2}}{(x - 3) (2 x + 3)} = 5 \Rightarrow 2 (4 x^{2} + 9 + 12 x) - 25 (x^{2} - 6 x + 9) = 5 (2 x^{2} - 3 x - 9) \Rightarrow 8 x^{2} + 18 + 24 x - 25 x^{2} + 150 x - 225 = 10 x^{2} - 15 x - 45 \Rightarrow 27 x^{2} - 189 x + 162 = 0 \Rightarrow x^{2} - 7 x + 6 = 0 \Rightarrow x^{2} - 6 x - x + 6 = 0 \Rightarrow x (x - 6) - 1 (x - 6) = 0 \Rightarrow (x - 1) (x - 6) = 0$

⇒ x – 1 = 0 or x – 6 = 0

⇒ x = 1 or x = 6

Thus, the solutions of the given equation are 1 and 6.

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