Solve for x: 2 over 5 plus 3 over 5 x equals quantity x plus 5 over 10?

Question

anonymous · Answer

$$\frac{2}{5}+\frac{3}{5x}=\frac{x+5}{10}$$??

deadshot · Answer

yes

deadshot · Answer

I've tried solving it, but I don't think there is a solution

deadshot · Answer

@campbell_st can you help me with this?

campbell_st · Answer

I'd multiply every term by 10x the common denominator of the 3 fractions

$$\frac{2}{5} \times 10x+ \frac{3}{5x} \times 10x = \frac{x +5}{10} \times 10x$$

this can be simplified to 

$$4x + 6 = x(x + 5)$$

which is the same as 

$$4x + 6 = x^2 + 5x$$

or 

$$x^2 + x - 6 = 0$$

this is a quadratic that can be solved by factoring 

hope this helps

deadshot · Answer

Thanks! The answer is (x-3)(x+2), right?

campbell_st · Answer

not quite you have 

(x -3)(x + 2) = 0

so what values can x take..?

deadshot · Answer

x can take -3 and 2, right?

campbell_st · Answer

nope... reverse the signs... because 

if x = 3

then (3 - 3) = 0

and 0 * (3 + 2) = 0

same for x = -2

substitute it and you get

(-2 -3)(-2 +2) = -5 * 0 = 0

deadshot · Answer

Oh, ok, now I get it, Thanks!

anonymous · Answer

so whats the answer because 0 is not one of the answer choices