Question

solve x
x+3/x+2 = 3x-7/2x-3


x is not equal to -2 and 3/2


guys it's urgent​

Answer 1

GIVEN :–

$\\\implies \bf \dfrac{x+3}{x+2}= \dfrac{3x-7}{2x-3}$

• And –

$\\\implies \bf x \neq - 2 \: \: and \: \:3/2$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\\\implies \bf \dfrac{x+3}{x+2}= \dfrac{3x-7}{2x-3}$

$\\\implies \bf (x + 3)(2x - 3) = (3x - 7)(x + 2)$

$\\\implies \bf 2 {x}^{2} - 3x + 6x - 9=3 {x}^{2} + 6x - 7x - 14$

$\\\implies \bf 2 {x}^{2} + 3x- 9=3 {x}^{2} - x- 14$

$\\\implies \bf 2 {x}^{2} + 3x- 9 - 3 {x}^{2} + x + 14 = 0$

$\\\implies \bf - {x}^{2} + 4x + 5= 0$

$\\\implies \bf {x}^{2} - 4x - 5= 0$

$\\\implies \bf {x}^{2} - 5x + x - 5= 0$

$\\\implies \bf x(x - 5) + 1(x - 5)= 0$

$\\\implies \bf (x + 1)(x - 5)= 0$

$\\\implies \large{ \boxed{ \bf x = 5, - 1}}$

Answer 2

☆Answer☆

(x+3)/(x+2) = (3x-7)/(2x-3)

(x+3)(2x-3) = (x+2)(3x-7)

2x^2-3x+6x-9 = 3x^2-7x+6x-14

2x^2-3x-9 = 3x^2-x-14

2x^2-3x-9-3x^2+x+14 = 0

-x^2+4x+5 = 0

x^2-5x+x-5 = 0

x(x-5)+1(x-5) = 0

(x-5) (x+1) = 0

(x-5) = 0

x = 5

and

(x+1) = 0

x = -1

Hence,

x = 5,-1

✔