Question

need help with this math question

Answer 1

\[\frac{ 2x }{ x+4 } +\frac{ x+1 }{ 2x }\]

Answer 2

@phi

Answer 3

do you know what would be a good common denominator?

Answer 4

4

Answer 5

one way to find a common denominator is to multiply the two separate denominators... don't bother to expand it, just write them next to each other.

Like this:
2x(x+4)

Answer 6

next, what do you multiply the first fraction by to make its bottom the common denominator 2x(x+4)?

Answer 7

2x?

Answer 8

yes. But we have to multiply both its top and bottom by 2x

Can you do that for the first fraction ?

Answer 9

yea hold on let me try

Answer 10

wouldnt it be this \[\frac{ 4x ^{2} }{ 2x(x+4) }\]

Answer 11

yes, looking good

next step, tackle the other fraction
what do we multiply its bottom by to make its bottom the common denominator?

Answer 12

yayy:)) umm we multiple 2x again right

Answer 13

if you multiply the second fraction's bottom by 2x you would get 2x*2x
we want the common denominator 2x(x+4)

Any other idea ?

Answer 14

x+1

Answer 15

if you multiply the bottom of the second fraction by (x+1) you would get
2x(x+1)
but we want 2x(x+4)

try again.

Answer 16

x+4 then

Answer 17

yes, because 2x(x+4) is what we want.

multiply the top and bottom of the second fraction by (x+4)

Answer 18

ok hold on

Answer 19

\[\frac{ (x+1)(x+4) }{ 2x(x+4) }\]

Answer 20

ok, so now we have
\[ \frac{4x^2}{2x(x+4)}+\frac{(x+1)(x+4)}{2x(x+4)} \]

you know that if we add two fractions that have the same bottom, we keep that bottom, and add the tops. Like this:
\[ \frac{4x^2+(x+1)(x+4)}{2x(x+4) }\]

Answer 21

yeah i know thanks for the help:)

Answer 22

we probably should expand (x+1)(x+4) and add up common terms

Answer 23

oh we suppose to do that

Answer 24

i dont think we have to do that

Answer 25

yes, people like to see the top simplified as much as possible.