Question

5/2x-4+2/x+3=3/x-2 how to solve this, our topic is function. ​

Answer 1

Step-by-step explanation:

$\frac{5}{2x - 4} + \frac{2}{x + 3} = \frac{3}{x - 2} \\ \\ taking \: lcm \: of \: on \: left \: side \\ \\ \frac{5(x + 3) + 2(2x - 4)}{(2x - 4)(x + 3)} = \frac{3}{x - 2} \\ \\ \frac{5x + 15 + 4x - 8}{(2 {x}^{2} + 6x - 4x - 12) } = \frac{3}{x - 2} \\ \\ \frac{9x + 7}{2 {x}^{2} + 2x - 12 } = \frac{3}{x - 2} \\ \\ (9x + 7)(x - 2) = 3(2 {x}^{2} + 2x - 12) \\ \\ 9 {x}^{2} - 18x + 7x - 14 = 6 {x}^{2} + 6x + 36 \\ \\ 9 {x}^{2} - 11x - 14 = 6 {x}^{2} + 6x + 36 \\ \\ 9 {x }^{2} - 6 {x}^{2} - 11x - 6x - 14 - 36 = 0 \\ \\ 3 {x}^{2} - 17x - 50 = 0 \\ \\ now \: for \: finding \: x \: use \: formula \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a } \\ \\ x = \frac{ - ( - 17)± \sqrt{ {( - 17)}^{2} - 4 \times 3 \times ( - 50) } }{2 \times 3} \\ \\ x = \frac{17± \sqrt{289 + 600} }{6} \\ \\ x = \frac{17 ± \sqrt{889} }{6} \\ \\ you \: can \: further \: calculate \: it \: otherwise \: it \: is \: ur \: ans$

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