Question

x+3/x+2=3x-7/2x-3 by quadratic formula​

Answer 1

Answer:

we want to transposs the RHS to rightside then solve it

Answer 2

Answer:

x = 5 or x = -1

Step-by-step explanation:

BOTH METHODS ARE Follows:-

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⇒ $\frac{x+3}{x + 2} =\frac{ 3x-7}{2x-3}$

Prime factorization method

⇒ (x+3)(2x-3)=(3x-7)(x+2)

⇒ 2x² - 3x + 6x - 9 = 3x² + 6x - 7x - 14

⇒ 2x² + 3x - 9 = 3x² - x - 14

⇒ 3x² - 2x² - x - 3x - 14 + 9 = 0

⇒ x² - 4x - 5 = 0

⇒ x² -5x + x - 5 = 0

⇒ x(x - 5) +1 (x - 5) = 0

⇒ (x - 5) (x + 1) = 0

⇒ x - 5 = 0 or x + 1 = 0

⇒ x = 5 or x = -1

===================================By Quadratic Formula:-

==================================

     x² - 4x - 5 = 0

a = 1, b = -4, c = -5

D = b² - 4ac = (-4)² - 4 (1) (-5)

                      = 16 + 20

                      = 36

now,

Quadratic formula

 x = -b ± √D / 2a

 = -(-4) ± √36 / 2(1)

 = 4 ± 6 / 2

∴ x = $\frac{4 + 6 }{2} and \frac{4-6}{2}$

  x = $\frac{10}{2} and \frac{-2}{2}$

  x = 5 and -1