Question

Please help, will medal

-3x 4
_____ + ______
x2 – 9 2x – 6

Answer 1

get them in terms of a common denominator
Start by factoring the left. recall that \(a^2-b^2=(a+b)(a-b)\)

Answer 2

please use these factorizations:
\[\begin{gathered}
{x^2} - 9 = \left( {x - 3} \right)\left( {x + 3} \right) \hfill \\
2x - 6 = 2\left( {x - 3} \right) \hfill \\
\end{gathered} \]

Answer 3

also 4/2x-6=2/x-3

Answer 4

oh ok

Answer 5

Then what @Michele_Laino

Answer 6

Using the factorization above, I get:
\[\frac{{ - 3x}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} + \frac{4}{{2\left( {x - 3} \right)}} = ...?\]

Answer 7

or, after a simplification:
\[\frac{{ - 3x}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} + \frac{2}{{\left( {x - 3} \right)}} = ...?\]

Answer 8

ok yes I understand that much, but I don't know what to do with the denominator :/

Answer 9

what is the least common multiple?

Answer 10

I've been very stressed and my brain just isn't understanding math lately, please remind me what a least common multiple is...

Answer 11

the least common multiple is:
(x-3)(x+3)

Answer 12

but why? I don't understand

Answer 13

OH!! I just remembered thank you

Answer 14

so does that mean you would have to multiple the right side by (x+3)?

Answer 15

since you have to pick common and uncommon factors with the highest exponent

Answer 16

it means that you have to multiply the numerator of the second fraction, by (x+3)

Answer 17

so multiply both the numerator and denominator by (x+3)?

Answer 18

here is:
\[\frac{{ - 3x}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} + \frac{2}{{\left( {x - 3} \right)}} = \frac{{ - 3x + 2\left( {x + 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}}\]

Answer 19

note that the numerator of the first fraction is unchanged

Answer 20

so, what is:
\[\frac{{ - 3x + 2\left( {x + 3} \right)}}{{\left( {x - 3} \right)\left( {x + 3} \right)}} = ...?\]

Answer 21

the denominator is x^2-9 right?

Answer 22

yes!

Answer 23

\[x^{2}-9\]

Answer 24

:) and I'm not sure about the numerator...

Answer 25

you have to compute the multiplication first

Answer 26

what is 2(x+3)=...?

Answer 27

2x+6

Answer 28

so it would be -x+6?

Answer 29

that's right!

Answer 30

THANK YOU SO MUCH

Answer 31

Thank you!