Question

questio

Answer 1

answer.

Answer 2

\[\frac{ 3x }{ x+2 }+1=\frac{ -6 }{ x+2 }\]

Answer 3

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

can you solve it now?

Answer 4

no i dont get how to

Answer 5

Adding fractions with common denominators?

Answer 6

can you at least simplify it?

Answer 7

how far are you getting?

Answer 8

i get \[3x^{2}+2\]

Answer 9

=?

Answer 10

Don't lose the equals sign if it's an equation.

Answer 11

-6

Answer 12

Ok, you have a nice mild quadratic equation there to solve.

Answer 13

Note that what's important here, is now that all the denominators are equal, then the numerators must be equal.
You'll have the restricted domain of x =/= -2 as well, so watch out for that.

Answer 14

so \[3x^{2}+2+6=0\]

Answer 15

Oh, hold up...

Answer 16

wait how did you get a quadratic

Answer 17

Bah, it's just addition. I think I had my eyes crossed there.

Answer 18

you shouldn't get a quadratic for this problem

Answer 19

I'm just going to show you the simplification steps

Answer 20

please take the time to understand them

Answer 21

if you have any questions ask

Answer 22

I have a question: Aren't those more steps than are necessary?

Answer 23

how do you get 6x

Answer 24

it was a mistake

Answer 25

From
\[\large \frac{3x}{x+2}+\frac{x+2}{x+2}=\frac{-6}{x+2}\]
\[\large \rightarrow 3x+x+2=-6, x \ne-2\]

Answer 26

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

\[\frac{3x + x + 2}{x+2} + \frac{6}{x+2} =0\]

\[\frac{3x + x + 2 + 6}{x+2} =0\]

Answer 27

now you can eliminate the denominator and solve very easily

Answer 28

how does x=-2

Answer 29

\[\large \rightarrow 4x=-8, x\ne-2\]
Therefore no solution?

Answer 30

cliffsedge I think you should be more descriptive why x=/= 2

yes
x = -2 is the solution you get but remember you cannot have a denominator of 0, what makes the denominator 0 in this equation?

Answer 31

i mean x =/= -2

Answer 32

^ @Australopithecus , yes, good point. I mentioned 'restricted domain' and had assumed that rachalh had already covered that concept elsewhere.

Answer 33

Another way of seeing it is to write it as a function
\[\large y=\frac{3x+x+2+6}{x+2} = \frac{4(x+2)}{x+2} \]
\[\large \rightarrow y=4, x\ne-2\]
And graph it and see that it is a horizontal line that will never cross the x-axis.

Answer 34

thank you