Perform the indicated operation.
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Question

Perform the indicated operation.
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anonymous · Answer

https://clackamasweb.owschools.com/media/g_ima01_2014/2/yplus5_yminus5.gif https://clackamasweb.owschools.com/media/g_ima01_2014/2/negyplus5_yminus5.gif https://clackamasweb.owschools.com/media/g_ima01_2014/2/yminus5_5minusy.gif

anonymous · Answer

@wio

anonymous · Answer

@TheRaggedyDoctor

zzr0ck3r · Answer

$\dfrac{y}{y-5}+\dfrac{5}{5-y}$

$\dfrac{(5-y)}{(5-y)}\dfrac{y}{y-5}+\dfrac{(y-5)}{(y-5)}\dfrac{5}{5-y}$

$=\frac{5y-y^2+5y-25}{(5-y)(y-5)}=\frac{-y^2+10y-25}{(y-5)(5-y)}=\frac{-y^2+5y+5y-25}{(y-5)(5-y)} \ = \frac{-y(y-5)+5(y-5)}{(y-5)(5-y)}=\frac{(y-5)(5-y)}{(y-5)(5-y)}=1$

anonymous · Answer

I dont have 1 in my choices

zzr0ck3r · Answer

your choices are wrong

zzr0ck3r · Answer

http://www.wolframalpha.com/input/?i=%5Cdfrac%7By%7D%7By-5%7D%2B%5Cdfrac%7B5%7D%7B5-y%7D+%3D+1

jim_thompson5910 · Answer

Another way to do it

$$\Large \frac{y}{y-5}+\frac{5}{5-y}$$

$$\Large \frac{y}{y-5}+\frac{5}{-1(-5+y)}$$

$$\Large \frac{y}{y-5}-\frac{5}{y-5}$$

$$\Large \frac{y-5}{y-5}$$

$$\Large 1$$

So $\Large \frac{y}{y-5}+\frac{5}{5-y}$ simplifies to $\Large 1$

anonymous · Answer

thank you

zzr0ck3r · Answer

his is much more clever ;) as always

zzr0ck3r · Answer

both of our answers should say that this is true as long as $y\ne 5$