Question

$\frac{x + 2}{2 - x} + \frac{x - 2}{2 + x} = 4 \frac{1}{4}$
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Answer 1

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\:\dfrac{x + 2}{2 - x} + \dfrac{x - 2}{2 + x} = 4\dfrac{1}{4}$

can be rewritten as

$\rm :\longmapsto\:\dfrac{x + 2}{2 - x} - \dfrac{2 - x}{x + 2} = 4\dfrac{1}{4}$

$\rm :\longmapsto\:\dfrac{ {(x + 2)}^{2} - {(2 - x)}^{2} }{(2 + x)(2 - x)} = \dfrac{17}{4}$

Please find the attachment

Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

• If Discriminant, D > 0, then roots of the equation are real and unequal.

• If Discriminant, D = 0, then roots of the equation are real and equal.

• If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

• Discriminant, D = b² - 4ac