So what did this student do wrong besides not showing all the work?

Question

anonymous · Answer

# 1?

anonymous · Answer

help anybody?

anonymous · Answer

i would give him a 0 coz he did everythin wrong

jim_thompson5910 · Answer

the student broke up the fraction completely wrong

jim_thompson5910 · Answer

you can't say

(a+b)/(c+d) = a/c + b/d

anonymous · Answer

I know the top does not = 1 & true true

jim_thompson5910 · Answer

the student somehow gets the right answer, but the intermediate step getting there is flawed

anonymous · Answer

& doesnt the denominator suppose to be with each side of the problem in order to work out?

jim_thompson5910 · Answer

so I would give 1 or 2 points for the correct answer, but leave off a lot of points for failing to show not that many steps

and the steps shown are wrong

anonymous · Answer

i was gonna put 2 points too lol :D

jim_thompson5910 · Answer

lol great minds think alike, so do you know how to get the correct answer (using the correct steps)?

anonymous · Answer

im saying! :D & sadly no >.<

jim_thompson5910 · Answer

ok we start with this expression

$$\large \frac{\sin^2(x) - \cos^2(x)}{\sin(x)+\cos(x)}$$

jim_thompson5910 · Answer

then factor the numerator using the difference of squares rule to get this

$$\large \frac{(\sin(x)+\cos(x))(\sin(x)-\cos(x))}{\sin(x)+\cos(x)}$$

jim_thompson5910 · Answer

see what to do from here?

anonymous · Answer

would the top =1 wait nevermind that wouldnt work>.< & wait so you cross out the + ones to get the - alone so thats how you would get the final answer right?

jim_thompson5910 · Answer

yep the "sin+cos" terms cancel leaving you with 

$$\large \sin(x)-\cos(x)$$

jim_thompson5910 · Answer

this shows the student got the right final answer at least

jim_thompson5910 · Answer

oh wait, that side is already given, hmm I guess the student already knew which answer to aim for

anonymous · Answer

oh snap! i finally get it dude!!!!! this is what imma do inmy test then just break the terms apart to get there easier ^-^ & lol im saying omg dude thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!:D

jim_thompson5910 · Answer

lol glad to be of help

jim_thompson5910 · Answer

and I'm glad it's all finally clicking

anonymous · Answer

I know me too! i hope i get at least an 80% on my test hopefully>.< & thanks again dude!:D

jim_thompson5910 · Answer

I'm sure you'll rock the test

anonymous · Answer

thanks!:D

jim_thompson5910 · Answer

yw