Question

Sorry if this is hard to understand. Fractions are hard to write.
((4)/(3a-5))+((3a^2+38a+36)/(25a-9a^3))=((3)/(3a+5))

Answer 1

ok

Answer 2

\[\frac{ 4 }{ 3a-5 } + \frac{ 3a^2+38a+36 }{ 25a-9a^2 } = \frac{ 3 }{ 3a+5 }\]

Answer 3

did i get that right?

Answer 4

Yeah

Answer 5

ok

Answer 6

yeah that looks right

Answer 7

i would multiply everything by a common denominator , so you can get rid of the fractions

Answer 8

oh thats a 9a^3 in the bottom right?

Answer 9

Yeah. its cubed. thats also part of the problem why i cant figure it out

Answer 10

\[25a-9a^3 = -a(9a^2 -25) = -a(3a-5)(3a+5)\]

Answer 11

Wouldn't you factor all of them

Answer 12

sometimes problems from books and homework give you clues, so i would have tried the other denominators (3a-5)(3a+5) as factors of the cubed term first

Answer 13

so multiply everything by -a(3a-5)(3a+5)

Answer 14

ok hang on one sec

Answer 15

ill starty typing it out

Answer 16

wait i should each fraction by the thing above or each denominator?

Answer 17

multiply both sides by a ratio of 1
\[\frac{ -a(3a-5)(3a+5) }{ -a(3a-5)(3a+5) }\]

Answer 18

all the fractions will be over the common denominator after that ,,

Answer 19

oh ok thanks

Answer 20

ill start typing it up

Answer 21

\[\frac{ -4a(3a+5) }{ -a(3a-5)(3a+5) } + \frac{ (3a^2+38a+36) }{ -a(3a-5)(3a+5) } = \frac{ -3a(3a-5) }{ -a(3a-5)(3a+5) }\]

Answer 22

see if you cancel out terms in the numerators and denominators, you are back to the starting problem

Answer 23

so now that everything is over a common denominator, you can equate the numerators, same as if you multiplied both sides by -a(3a-5)(3a+5) to cancel the denominators,

Answer 24

\[-4a(3a+5) + (3a^2+38a+36) = -3a(3a-5)\]

Answer 25

multiply out the terms, and combine like powers

Answer 26

\[-12a^2 - 20a +3a^2+38a+36 = -9a^2+15a\]

Answer 27

u with me ?

Answer 28

Yeah I follow.

Answer 29

see the a^2 terms cancel , you have -9a^2 on both ends

Answer 30

you left with 18a+36=15a which leads to 3a=-36 which means a = 12

Answer 31

-12

Answer 32

i mean negative 12

Answer 33

ill do a quick chek on my calc to see if any mistakes were made.. one sec

Answer 34

I think that's right because -12 is answer b

Answer 35

yep a=-12 is it

Answer 36

Thanks!

Answer 37

welcome, anytime

Answer 38

just remember if it is a prob from a book or test or something, and you need to factor to get a common denominator, look at the other denominators as they are probably the factors..

Answer 39

like the (3a-5)(3a+5) in this prob

Answer 40

ok got it