Question

Need help step by step
check comment below

Answer 1

\[\frac{ -2x }{ x+2 }+\frac{ x }{ 3 \ }= \frac{ 4}{ x+2 }\]

Answer 2

I'm not that great with these but give me a second i think i can do it.

Answer 3

So, I guessing you have to solve for x?

Answer 4

she wants step by step

Answer 5

i have the answer but trying to find a simple way to explain it.

Answer 6

x=0,16 thats the answer but i dont know how to explain how i got it.

Answer 7

Ok thanks for trying @Isaac.Tillman03

Answer 8

Youre welcome but let me try to explain it i dont want to leave you hangin

Answer 9

To find x, you can start by adding the fractions on the left. Like so, \[\frac{ x }{ 3 } - \frac{ 2x }{ x+2 } = \frac{ 4 }{ x+2 }\]

Answer 10

Adding them we have, \[\frac{ x(x+2) - 3(2x) }{ 3(x+2) } = \frac{ 4 }{ x+2 }\]

Answer 11

Opening brackets on the left side we have, \[\frac{ x^{2}+2x-6x }{ 3x+6 } = \frac{ 4 }{ x+2 }\]

Answer 12

\[\frac{ x^{2}-4x }{ 3x+6 } = \frac{ 4 }{ x+2 }\]

Answer 13

Good Job @Isaiah.Feynman

Answer 14

We could factor the numerator and denominator on the left side to get \[\frac{ x(x+2)(x-2) }{ 3(x+2) }\]

Answer 15

We can now cancel out the x+2 to get \[\frac{ x(x-2) }{ 3 } = \frac{ 4 }{ x+2 }\]

Answer 16

We could cross multiply to get \[x(x-2)(x+2) = 12\]

Answer 17

Well, could you solve for x from here?

Answer 18

\[x+2 \neq 0,x \neq -2\]
\[\frac{ x }{ 3 }=\frac{ 4 }{ x+2 }+\frac{ 2x }{ x+2 }\]
\[\frac{ x }{ 3 }=\frac{ 4+2x }{ x+2 }\]
cross multiply
\[x(x+2)=(4+2x)(3)\]
\[x^2+2x=12+6x\]
\[2x^2+2x-12-6x=0\]
x^2-4x-12=0
\[x^2-6x+2x-12=0\]
\[x(x-6)+2(x-6)=0\]
\[(x-6)(x+2)=0,x=6,x=-2\]
rejecting x=-2,
x=6