Question

Prove that 2x/x-3+1/2x+3+3x+9/(x-3)(2x+3)=0

Answer 1

Answer:

Obviously, the given equation is valid if

x - 3≠0 and 2x + 3≠0.

Multiplying throughout by (x - 3) (2x - 3), we get

2x(2x + 3) + 1(x - 3) + 3x + 9 = 0 or

4x2 + 10 + 6 = 0 or

2x2 + 5x + 3 = 0 or

(2x + 3) (x + 1) = 0

But 2x + 3≠ 0, so we get

x + 1 = 0.

This gives x = - 1 as the only solution of the given equation.

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Answer 2

Answer:

Step-by-step explanation:

Solution :-

Here, we have

⇒ 2x/(x - 3) + 1/(2x + 3) + (3x + 9)/(x - 3) (2x + 3) = 0

By Multiplying throughout by (x - 3) (2x + 3), we get

⇒ 2x(2x + 3) + (x - 3) + 3x + 9 = 0

⇒ 4x² + 6x + x - 3 + 3x + 9 = 0

⇒ 4x² + 10x + 6 = 0

Divining eq by 2, we get

⇒ 2x² + 5x + 3 = 0

By using factorization method, we get

⇒ 2x² + 5x + 3 = 0

⇒ 2x² + 2x + 3x + 3 = 0

⇒ 2x(x + 1) + 3(x + 1) = 0

⇒ (x + 1) (2x + 3) = 0

⇒ x + 1 = 0 or 2x + 3 = 0

⇒ x = - 1, - 3/2

Here, x = - 1, - 3/2.