Question

(2/5) + (3/5x) = (x + 5/10)
The answer is NOT x = 2, as I originally thought.

Answer 1

LCD is 10x.
4x/10x + 6/10x = x^2 + 5x/10x
4x + 6 = x^2 + 5x
0 = x^2 + x - 6
Where to from there? Factoring?

Answer 2

That would give me 0 = (x - 2)(x + 3), correct? And the solutions would be x = 2, x = -3. Now I would need to plug them back in.

Answer 3

2/5 + 3/10 = 7/10

Answer 4

2/5 x 2/2 to create a common denominator...4/10 + 3/10 = 7/10. This is true. Now we check -3.

Answer 5

2/5 + 3/-15 = 2/10...need -15 as the LCD

Answer 6

Wouldn't x= -1/4 ?

Answer 7

I don't have any fractions in my answers...and the LCD wouldn't be -15. Hm.

Answer 8

@absurdism Come back, please? I'm stuck. :)

Answer 9

-3 pretty much has to work when you plug it back in...but I'm trying to find the LCD so I can check it.

Answer 10

(I say that it has to work, because my options are no solutions, 2, -3, or 2 and -3, and I know that 2 works but 2 is not the only answer, thus no solutions can't be the answer, so I have to make sure -3 works).

Answer 11

sorry, is the equation 2/5 + 3/(5x) = x + 5/10?

plus if you have solved the equation by factoring you needn't do anything else

Answer 12

Yes, that is the equation. But I have to check my work. :)

Answer 13

To make sure it's not an extraneous solution.

Answer 14

it must be 2 and -3
(x-2)(x+3) = x^2 + 3x - 2x - 6
= x^2 + x - 6

Answer 15

that's as much work check as you need

Answer 16

Okay. Thank you!

Answer 17

no worries

Answer 18

@absurdism Can you help with a slightly harder one? Same topic.

Answer 19

mhm