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Algebra Level 4

$\large\frac{6-x}{x^{2}-4} = 2 + \frac{x}{x+2}$

Find the number of real solutions of the equation above.

3 1 2 0

1 solution

Shivam Jadhav
Jun 22, 2015

First we solve we get $\frac{6-x}{x^{2}-4}=\frac{3x+4}{x+2}$ . $\frac{6-x}{x-2}=3x+4,$ By solving further we get $3x^{2}-x-14=0$ From this we get $x=\frac{7}{3},-2$ but if we put $x=-2$ in the equation given in the question it becomes undefined. Therefore number of real solutions is $\boxed{1}$ .

Great problem. I got caught in the $x = -2$ (because I was too lazy to check the values lol).

FYI, the solution would be much more friendly if you used $\backslash( \quad \backslash)$ around the less important equations instead. Not everything needs to appear on its own line. EG the comma and the fullstop.

Calvin Lin Staff - 5 years, 11 months ago

Why have cancelled one root in your second step,which led to elimination of a root. Given equation is a polynomial of degree 3

Akhil Bansal - 5 years, 11 months ago

$x^2-4$ can be rewritten as $(x+2)(x-2)$

Vishnu Bhagyanath - 5 years, 11 months ago

If we don't cancel the (x+2) we will get 3 real solutions

Naman Kapoor - 5 years, 11 months ago

It's Easy peasy

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