subtracting a rational function , help ?

Question

anonymous · Answer

$$\frac{ 3 }{ 2x } -\frac{ 9 }{ 2 } = 6x$$

agent0smith · Answer

Get common denominators, as you learned yesterday ;)

anonymous · Answer

but i get confused on as how to get the common denominator when its comes to multiplying/dividing and adding/subtracting :/

agent0smith · Answer

Well what's missing from the right fraction?

anonymous · Answer

an x ?

agent0smith · Answer

So fix that :D

anonymous · Answer

so what happens to the 6x ?

anonymous · Answer

do i multiply 6x by 2x since the denominator is 1 ?

agent0smith · Answer

Leave 6x alone for now

anonymous · Answer

$$\frac{ 3 }{ 2x } - \frac{ 9x }{ 2x }= 6x$$

anonymous · Answer

okay so now what ?

agent0smith · Answer

Do stuff! You know how to subtract them! :P

anonymous · Answer

well i cant subtract 3 from 9x because theyre not like terms

agent0smith · Answer

That doesn't mean you can't combine (subtract) the fractions

anonymous · Answer

3 - 9x = 6x ?

agent0smith · Answer

No, just put them over a common denominator.

agent0smith · Answer

That's why you got a common denominator of 2x, remember.

anonymous · Answer

$$\frac{ 3-9x }{ 2x }$$

agent0smith · Answer

Correct. It equals 6x. Now, multiply both sides by 2x, to get rid of that denominator.

anonymous · Answer

3 - 9x = 12^2

agent0smith · Answer

12x^2? yes.

anonymous · Answer

oh yeh i forgot the x sowwy , but now its a regular quadratic equation right ?

agent0smith · Answer

$$\Large 3-9x = 12x^2$$now get it equal to zero, and solve for x. It will be a quadratic.

agent0smith · Answer

Btw to make it easier, divide *everything* by the common factor of 3.

anonymous · Answer

$$    4x^2 + 3x - 1 = 0 $$

agent0smith · Answer

Awesome, now solve either by factoring or quadratic formula!

anonymous · Answer

ima try the quadratic formula because i dont like factoring when a has a coefficient greater than 1 :p

agent0smith · Answer

Yeah it sucks. Start by multiplying the first and last numbers, 4*-1 = -4

find two numbers that multiply to -4 and add up to the middle number 3... which... there aren't any. Screw factoring.

anonymous · Answer

haha i got x = 1/4 & -1 (:

agent0smith · Answer

You're right.

anonymous · Answer

thank you so much (:

agent0smith · Answer

Welcome as always <3

agent0smith · Answer

Oh wow it does factor, lol " two numbers that multiply to -4 and add up to the middle number 3"

+4 and -1 oops.