Simplify the complex fraction:

(Problem in comments...)

Question

Simplify the complex fraction:

(Problem in comments...)

anonymous · Answer

$$\frac{ \frac{ \frac{ 1 }{ a+1 } +2}{ 1 } }{ a+7 } +7$$

ganeshie8 · Answer

work numerator separately first
work denominator separately next

after flip the denominator to convert it to multiplication

anonymous · Answer

so the 2 & 7, turns into 2/1 & 7/1?

ganeshie8 · Answer

$\huge      \dfrac{ \dfrac{ \frac{ 1 }{ a+1 } +2}{ 1 } }{ a+7 } +7$


Make the common denominators on numerator and denominator separately :

$\huge      \dfrac{ \dfrac{ \frac{ 1 }{ a+1 } +\frac{2(a+1)}{a+1}}{ 1 } }{ a+7 } +\frac{7(a+7)}{a+7}$

ganeshie8 · Answer

add both fractions on numerator,
add both fraction on denominator

ganeshie8 · Answer

what do u get ?

anonymous · Answer

2a +2/a+1 & 7a+49/a+7

ganeshie8 · Answer

Excellent !

anonymous · Answer

do I add the 1 to both?

ganeshie8 · Answer

$\huge      \dfrac{ \dfrac{ \frac{ 1 }{ a+1 } +2}{ 1 } }{ a+7 } +7$


Make the common denominators on numerator and denominator separately :

$\huge      \dfrac{ \dfrac{ \frac{ 1 }{ a+1 } +\frac{2(a+1)}{a+1}}{ 1 } }{ a+7 } +\frac{7(a+7)}{a+7}$


Adding fractions on numerator and denominator gives :

$\huge      \dfrac{  \frac{ 2a+2 }{ a+1 } } { \frac{1+7a+49}{a+7}}$

ganeshie8 · Answer

right ?

anonymous · Answer

yea, but what about the 1+ in front of the 2 too?

ganeshie8 · Answer

Good :) was just checking if you're alert or not ;)

ganeshie8 · Answer

let me correct it

ganeshie8 · Answer

$\huge      \dfrac{ \dfrac{ \frac{ 1 }{ a+1 } +2}{ 1 } }{ a+7 } +7$


Make the common denominators on numerator and denominator separately :

$\huge      \dfrac{ \dfrac{ \frac{ 1 }{ a+1 } +\frac{2(a+1)}{a+1}}{ 1 } }{ a+7 } +\frac{7(a+7)}{a+7}$


Adding fractions on numerator and denominator gives :

$\huge      \dfrac{  \frac{ 1+2a+2 }{ a+1 } } { \frac{1+7a+49}{a+7}}$

anonymous · Answer

I'm always alert at 4 am lol

ganeshie8 · Answer

lol, see if that looks okay now...

anonymous · Answer

yes!

ganeshie8 · Answer

good :)
above expression is same  as :

$\huge      \dfrac{  \frac{2a+3 }{ a+1 } } { \frac{7a+50}{a+7}}$

ganeshie8 · Answer

lastly, flip the denominator to convert it to multiplicaiton

ganeshie8 · Answer

$\huge      \dfrac{  \frac{2a+3 }{ a+1 } } { \frac{7a+50}{a+7}}$


is same as :


$\huge      \frac{2a+3 }{ a+1 }  \times \frac{a+7}{7a+50}$

ganeshie8 · Answer

putting everything under same fraction gives :

$\huge      \frac{(2a+3)(a+7) }{ (a+1)(7a+50) }  $

ganeshie8 · Answer

we're done !

anonymous · Answer

That's it?

ganeshie8 · Answer

thats it, thats the final simplified form

anonymous · Answer

Why is there sooo many people watching us solve this problem? lol

ganeshie8 · Answer

cuz you're a brilliant student... everyone likes to help u :)

anonymous · Answer

Lol they're just staring lmaooo

ganeshie8 · Answer

thats one of acknowledging the fact that you're doing it correctly and they dont need to pitch in to rescue u lol

anonymous · Answer

Lol, that's kind of creepy lol but it's cool lol

anonymous · Answer

This one is marked incorrect...

ganeshie8 · Answer

oh, take a snapshot of question and attach

anonymous · Answer

ok...hold on

ganeshie8 · Answer

kk

anonymous · Answer

attachment

ganeshie8 · Answer

Ahh, there was a mismatch in the questions between ur snapshot and the one u posted here

ganeshie8 · Answer

the snapshot has $\large  (a+1)$    on bottom of both fractions,

ganeshie8 · Answer

but the question u typed here has :

$\huge      \dfrac{ \dfrac{ \frac{ 1 }{ a+1 } +2}{ 1 } }{\color{red}{ a+7} } +7 $

ganeshie8 · Answer

they're not same :/

anonymous · Answer

Ooooooooooh, I see it ! Ooooops 😣

ganeshie8 · Answer

Yes !

anonymous · Answer

So, how do we solve this one?

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=simplify+%281%2F%28a%2B1%29%2B2%29%2F%281%2F%28a%2B1%29%2B7%29

anonymous · Answer

Thank you !