Question

@ganeshie8

I have a few questions about this problem if you don't mind...? When i'm factoring... say a problem looks like this
\[\frac{ 4 }{ m+9 } + \frac{ 5 }{ m^2 - 81}\]

\[\frac{ 4 }{ m+9 } + \frac{ 5 }{ (m+9)(m-9) }\]

Does the m+9 on the LHS stay the same or can that somehow be factored and do I have to factor the 4 and the 5 or do those stay the same? Or do I get a common denominator and then touch the numerators?

Answer 1

Since u have two fractions,
to add them, they must have same denominators.

Answer 2

So, multiply and divide first fraction wid \((m-9)\)

Answer 3

\(\large \frac{ 4 }{ m+9 } + \frac{ 5 }{ (m+9)(m-9) }\)

\(\large \frac{ 4 }{ m+9 }\color{green}{\frac{m-9}{m-9}} + \frac{ 5 }{ (m+9)(m-9) }\)

Answer 4

now both fractions have same denominator,
so u can add the numerators

Answer 5

\(\large \frac{ 4 }{ m+9 } + \frac{ 5 }{ (m+9)(m-9) }\)


\(\large \frac{ 4 }{ m+9 }\color{green}{\frac{m-9}{m-9}} + \frac{ 5 }{ (m+9)(m-9) }\)


\(\large \frac{ 4(m-9) + 5}{ (m+9)(m-9) }\)

Answer 6

simplify the numerator

Answer 7

let me knw if something doesnt make sense :)

Answer 8

o.o I think it makes sense so far

Answer 9

good, simplify the numerator and we're done!

Answer 10

Do I use distributive property and then add 5 to it?

Answer 11

exactly !

Answer 12

Um...
\[\frac{ 4m - 36 +5 }{ (m+9)(m-9) }\]

I'm not sure whether or not I actually add the 5 or leave it alone but if I do add it

\[\frac{ 4m - 31 }{ (m-9)(m+9) }\]

And thank you for the positive testimonial c:

Answer 13

are you trying to factor out a m+9, or trying to combine the rational expressions?

Answer 14

Looks good, and yes always combine like terms and simplify...

Answer 15

Thank you and I think I'm supposed to be combining rational expressions. I'm not sure... what's the difference between the two if you don't mind me asking?

Answer 16

np.. u wlc :) there is a slight difference... if you're asked to factor out oly (m+9), then u dont need to simplify further...

but here they asked you to combine the rational expressions... so u must factor, get same denominators, add numerators and simplify.

Answer 17

Ohhh that makes sense lol thank you.
Psssst!
*I'm combining rational expressions guys*
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