Question

solve the following equation by factorisation
3x-3/2x-3 = 3x-8 / x+4 a question from quadratic equation chapter. please also flw me guys on brainly.​

Answer 1

Step-by-step explanation:

$\frac{3x - 3}{2x - 3} = \frac{3x - 8}{x + 4}$

$\scriptsize(x + 4)(3x - 3) = (3x - 8)(2x - 3)$

$\scriptsize{x(3x - 3) + 4(3x - 3) = 3x(2x - 3) - 8(2x - 3)}$

$\scriptsize3 {x}^{2} - 3x + 12x - 12 = 6 {x}^{2} - 9x - 16x + 24$

$\scriptsize3 {x}^{2} + 9x - 12 = 6 {x}^{2} - 25x + 24$

$\scriptsize0 = 6 {x}^{2} - 25x + 24 - 3 {x}^{2} - 9x + 12$

$\scriptsize0 = 6 {x}^{2} - 3 {x}^{2}- 25x - 9x + 24 + 12$

$0 = 3 {x}^{2} - 34x + 36$

$or \: \: \: \: 3 {x}^{2} - 34x + 36= 0$

Comparing the equation with ax² + bx + c = 0,

$a = 3 , \: b = -34 , \: c = 36$

$\scriptsize{ \bold{{Substituting \: the \: value \: in \: the \: formula}}} \\ \bold{ \: x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2} ,}$

$\bold{x = \frac{ - ( - 34)± \sqrt{ {( - 34)}^{2} - 4(3)(36)} }{2} }$

$\bold{ x = \frac{34± \sqrt{1156 - 4(108)} }{2} }$

$\bold{ x = \frac{34± \sqrt{1156 - 432} }{2} }$

$\bold{ x = \frac{34± \sqrt{724} }{2} }$

On taking the (+) sign.

$\bold{ x = \frac{34 + \sqrt{724} }{2} }$

On taking the (–) sign.

$\bold{ x = \frac{34 - \sqrt{724} }{2} }$

I hope it is helpful