Question

Find the solution of the following equation. 2/(x+3) - 4/(x-3) = -6/(x+3)

Answer 1

QUESTION-:

Find the solution of-:

$\bf\; \frac{2}{x+3}-\frac{4}{x-3}=\frac{-6}{x+3}$

EXPLANATION-:

Multiply both sides by the Least Common Denominator: (x+3)(x-3)

$\rightarrow \bf\; \bf\;(x+3)(x-3) \times\frac{2}{x+3}-(x+3)(x-3) \times\frac{4}{x-3}=(x+3)(x-3) \times\frac{-6}{x+3}\\\\\rightarrow \bf\; 2(x-3)-4(x+3)=-6(x+3)\\\\\rightarrow \bf\; -2x-18=-6x-18\\\\\rightarrow \bf\; -2x=-6x\\\\\rightarrow \bf\; x=3x\\\\\rightarrow \bf\; 0=3x-x\\\\\rightarrow \bf\; 0=2x\\\\\longrightarrow \underline{\boxed{\underline\boxed{\bigstar\bf\; \;x=0 \bigstar}}}}$

∴The value of x is 0

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Answer 2

★ Solution :-

The given equation is,

$\sf \leadsto \dfrac{2}{(x + 3)} - \dfrac{4}{(x - 3)} = \dfrac{ - 6}{(x + 3)}$

$\sf \leadsto - \dfrac{4}{(x - 3)} = \dfrac{ - 6}{(x + 3)} - \dfrac{2}{(x + 3)}$

$\sf \leadsto - \dfrac{4}{(x - 3)} = \dfrac{ - 6 - 2}{(x + 3)}$

$\sf \leadsto - \dfrac{4}{(x - 3)} = \dfrac{ - 8}{(x + 3)}$

$\sf \leadsto 4(x + 3) = - 8(x - 3)$

$\sf \leadsto 4x + 12 = - 8x + 24$

$\sf \leadsto 4x + 8x = 24 - 12$

$\sf \leadsto 12x = 12$

$\sf \leadsto x = \dfrac{12}{12}$

$\sf \leadsto x = 1$

Therefore, the value of x is 1.