Question

solve for x. given that x is not equal to -3 and half​

Answer 1

✨✨✨✨Thanks for asking ✨✨

here is your answer

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

think that

$\frac{2x + 3}{x + 3} = a \\ so \: \frac{x + 3}{2x + 3} = \frac{1}{a}$

so ,

$2a - 3 \times \frac{1}{a} = 5 \\ => 2a - \frac{3}{a} = 5 \\ = > \frac{2 {a}^{2} - 3 }{a} = 5 \\ => 2 {a}^{2} - 3 = 5a \\ = > 2 {a}^{2} - 5a - 3 = 0 \\ = > 2 {a}^{2} - 6a + a - 3 = 0 \\ = > 2a(a - 3) + 1(a - 3) \\ = > (2 a+ 1)(a - 3) = 0\\ \\ so \: \: \: 2a + 1 = 0 \\ = > 2a = - 1 \\ = > a = \frac{ - 1}{2} \\ \\ or \: \: \: \: = > a - 3 = 0 \\ = > a = 3$

the answers are

$the \: answers \: are \: \frac{ - 1}{2} or \: 3$

✨✨ hope it helps✨✨

Answer 2

2$\frac{2x-1}{x+3}$-3$\frac{x+3}{2x-1}$ = 5 (given/question)

⇒$\frac{2(2x-1)(2x-1)-3(x+3)(x+3)}{(x+3)(2x-1)}$ = 5 (by taking LCM to make denominator common)

⇒ 2(2x-1)² -3(x+3)² = 5(x+3)(2x-1)

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

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

⇒5x²- 26x - 25 = 10x² + 25x - 15

⇒5x² - 26x - 25 - 10x² - 25x + 15 = 0

⇒ -5x² - 51x -10 = 0

Using quadratic formula, ((-b±$\sqrt{b^{2}-4ac }$)/2a))

(51±$\sqrt{2601-4(-5)(-10)}$)/(-10)

(51±$\sqrt{2401}$)/-10

⇒ $\frac{51+49}{-10}$ or $\frac{51-49}{-10}$

⇒ -10 or $\frac{-1}{5}$