Question

can someone help me with solving a rational equation ?

Answer 1

\[\frac{ 3 }{ 2x } - \frac{9 }{ 2 }= 6x\]

Answer 2

try multiplying throughout by 2x to eliminate the denominators altogether..

Answer 3

\[3-9x=8x^{2}\]

Answer 4

this is done by multiplying 2x to both sides

Answer 5

@hartnn it says i have to find a common denominator first

Answer 6

shud be 12 x ^2

Answer 7

ok, that u get by finding LCM of all the denominators
whats LCM of 2x and 2 ?

Answer 8

so 6x doesnt have a denominator of 1 ?

Answer 9

it has....
ok find LCM of 2x,2,1

Answer 10

wouldnt i make every denominator equal to 2x ( 2 ) ( 1 ) ? like when i add/subtract a rational function ?

Answer 11

that you can but thats not the standard/simplest thing to do,
like for
1/6+1/8 , you don't so
8/ (6*8) + 6/(6*8)

LCM of 6,8 is 24
so you actually do
4/6*4 + 3/8*3 = 4/24 + 3/24 = 7/24

Answer 12

you don't do**

Answer 13

oh i see i see

Answer 14

so the lcm is 1 ?

Answer 15

no....GCD is 1
you know how to find LCM ?

Answer 16

2x = 2*x*1
2 = 2*1

common part = 2*1
uncommon part = x
LCM = common * uncommon = 2*1*x = 2x
thats how i find.....idk how u find it...

Answer 17

so you need to make common denominator as 2x
no change in 1st term as denom = 2x
2nd term denom = 2
so you will multiply and divide by x

9/2 = 9x/2x

so for left side we got a common denominator
3/2x - 9x/2x = ....

Answer 18

so the lcm is common * uncommon ?

Answer 19

thats not the standard way (or it maybe, idk) but thats how i find it....

Answer 20

ok i see it now thank you. so what about the 6x ?

Answer 21

the denominator =1
to make it 2x
what you need to do ?

Answer 22

multiply it by 2x

Answer 23

not only multiply , we cannot change the term
we need to multiply and divide

6x = 6x*2x /2x

Answer 24

and the numerator as well which is 12x^2 / 2x ?

Answer 25

yes

Answer 26

now we have same numerator everywhere, we can equate the numerators :)

Answer 27

same denominator **

Answer 28

ok so my equation looks like \[\frac{ 3 }{ 2x } - \frac{ 9x }{ 2x } = \frac{ 12x^2 }{ 2x }\]

Answer 29

yes it does

Answer 30

ok so now ima focus on 3 - 9x = 12x^2 right ?

Answer 31

absolutely

Answer 32

thats just a quadratic equation
can u solve it ?

Answer 33

oh yeh you right , ima just move the 12x^2 to the left side and set it equal to 0 right ?

Answer 34

yes

Answer 35

ok ima try to solve it right now

Answer 36

i cant find two numbers that when multiplied give me 9 and when added give me -3

Answer 37

and what about 12 ?
that is used only if the co-efficient of x^2 is 1

Answer 38

but first i will suggest you simplify it by dividing throught by 3

Answer 39

3-9x -12x^2 = 0
-3 (4x^2 +3x -1) = 0

4x^2 +3x -1 = 0
find 2 numbers with sum = +3 and product = 4*-1 = -4

Answer 40

because in ax^2+bx+c =0 we find 2 numbers with sum = +b and product = a*c

Answer 41

i got to go, i'll check back later whether u got correct 2 values of x
you can also verify by plugging the values you got in the original equation and checking whether left side = right side or not