Question

4/x-3=5/2x+3


solve using factorisation method​

Answer 1

Answer:

4/x-3=5/2x+3

=4/x-5/2x=6

3/2x=6

3=12x

x=4

Answer 2

GIVEN :

$\frac{4}{x} - 3 = \frac{5}{2x + 3}$

TO FIND :

The value of X using factorisation method.

SOLUTION :

$⟶ \frac{4}{x} - 3 = \frac{5}{2x + 3}$

$⟶ \frac{(4 - 3x)}{x} = \frac{5}{2x + 3}$

Now cross multiply :-

$⟶ (4 - 3x)(2x + 3) = 5x$

$⟶ 8x + 12 - 6 {x}^{2} - 9x = 5x$

$⟶ 8x + 12 - 6 {x}^{2} - 9x - 5x = 0$

$⟶ 12 - 6 {x}^{2} -6 x = 0$

taking out -6 as common we get =>

⟶ ${x}^{2} + x - 2 = 0$

Now we will factorize by using middle term factorisation method :-

⟶ ${x}^{2} + 2x - x - 2 = 0$

now taking out common=>

⟶ $x(x + 2) - 1(x + 2) = 0$

taking out (x+2) as common ⟶

⟶ $(x - 1)(x + 2) = 0$

Therefore x = 1 or X = -2

ANSWER :

X = 1 or -2