Question

Solve by factorization method: (4/x ) -3 = 5/(2x+3) , x≠ 0, -3/2.

Answer 1

Answer:

The solution of the expression is x=-2 and x=1.    

Step-by-step explanation:

Given : Expression $(\frac{4}{x})-3=\frac{5}{2x+3}$

To find : Solve by factorization?

Solution :

Solve the expression,

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

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

Cross multiply,

$(4-3x)(2x+3)=5x$

$8x+12-6x^2-9x=5x$

$6x^2+6x-12=0$

$x^2+x-2=0$

Apply middle term split,

$x^2+2x-x-2=0$

$x(x+2)-1(x+2)=0$

$(x+2)(x-1)=0$

$x=-2,1$

Therefore, The solution of the expression is x=-2 and x=1.

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Here, we have

⇒ 4/x - 3 = 5/2x + 3

⇒ 4 - 3x/x = 5/2x + 3

⇒ (4 - 3x) (2x + 3) = 5x

⇒ 12 - x - 6x² = 5x

⇒ 6x² + x - 12 = 0

Dividing eq by 6, we get

⇒ x² + x - 2 = 0

By using factorization method, we get

⇒ x² + x - 2 = 0

⇒ x² + 2x - x - 2 = 0

⇒ x(x + 2) - 1(x + 2) = 0

⇒ (x + 2) (x - 1)

⇒ x + 2 = 0 or x - 1 = 0

⇒ x = - 2, 1 (As x can't be negative)

⇒ x = 1

But here, x = - 2, 1