Question

Can someone please help me to answer this math question? Please? I will fan and give a medal...
Please help me to simplify this Rational Expression -
4x+2 10x-1 2x-3
----- + ------ + ------
5x 20x 4x

Answer 1

@AmTran_Bus could you please try to help me with this question?

Answer 2

Type it into wolfram alpha (google that). Cant right now sorry.

Answer 3

oh okay

Answer 4

@phi can you help me with this question please?

Answer 5

I would use a common denominator of 20x

Answer 6

yes sir

Answer 7

that means multiply the first fraction by 4/4

Answer 8

so multiply by 4?
4x+2
----- * 4?
5x

Answer 9

not by 4, by \[ \frac{4}{4} \]

Answer 10

oh ok

Answer 11

what do I do with the 4x+2? do I go ahead and add the 2 to the 4?

Answer 12

the top becomes (4x+2)*4

that is 4 x's plus a 2
x+x+x+x+1+1 if we expand it out
(of course we usually write that as 4x+2)

Answer 13

4* (4x+2) means you have 4 of the (4x+2)
people use the "distributive law" to multiply 4 times each "thing" inside the parens

but its good if you have an idea that helps to remember what to do.

think of the parens as a package with stuff inside it, and you have 4 of these packages
if you have that idea, it makes sense that you have 4 of each thing inside

or if we write it out
4(4x+2) = 4*4x + 4*2 = 16x+8

Answer 14

ok so
4x+2 4 16x+8
----- * --- = -------
5x 4 20x
?

Answer 15

@phi ?

Answer 16

yes. Let's skip the middle fraction for now (it already has 20x in the bottom)
any idea what to multiply the bottom of the last fraction to make it 20x ?

Answer 17

6?

Answer 18

try it: 6*4x= ?

Answer 19

5 sorry

Answer 20

yes, 5 looks good
if we multiply the bottom by 5, then we have to multiply the top by the same thing i.e. 5
can you multiply the top by 5 ?

Answer 21

10x-15?

Answer 22

yes. now all 3 fractions have the same bottoms
that means we can add the "tops" and put that over 20x to get the answer

so we add up
16x + 8
10x - 1
10x - 15

can you do that ?
you add the numbers "normally"

for the x terms: think like this: 16 x's plus 10 x's plus 10 more x's
how many x's is that all together?

Answer 23

36x?

Answer 24

yes. and the numbers 8 -1 -15 ?

Answer 25

8? or -8?

Answer 26

-8. if numbers have the same sign like this: -1 -15
then you can add them up and make the answer negative: -16
you now have
8 - 16
if you have two numbers with different signs
subtract big - small: 16-8 = 8
then make it the sign of the "big" number (-16). we get -8

Answer 27

so the answer so far is
\[ \frac{36x-8}{20x} \]

finally notice we can "factor out" 4 from the top. (this is the opposite of distributing)
\[ \frac{4(8x-2)}{20x} \]
now divide top and bottom by 4 to simplify

Answer 28

* \[ \frac{4(9x-2)}{20x}\]

Answer 29

you should get
\[ \frac{9x-2}{5x}\]

Answer 30

thank you so much!! I really understand how to add them now!