How do you know if you have to factor a quadratic expression to solve a rational equation?

Question

anonymous · Answer

You don't ;D

hartnn · Answer

For, $ax^2+bx+c$

If discriminant 
$D = b^2-4ac$
is a PERFECT SQUARE

only then, you can factor your quadratic expression into integral factors.

anonymous · Answer

Can you show me with this problem?
1/t-2=t/8

hartnn · Answer

is "t-2" in the denominator ??
then multiply throughout by t-2

if only "t" is in the denominator, then multiply throughout by 't'

anonymous · Answer

The answers are -2,4 . But how do they get that?

hartnn · Answer

so its (t-2)

1/(t-2)=t/8

hartnn · Answer

multiply both sides by 8(t-2)

8 = t (t-2)

got this ?

anonymous · Answer

Yes

hartnn · Answer

so
t^2 -2t -8 = 0

do you know how to solve this quadratic ?

anonymous · Answer

Still confused, Can you write it out step by step?

hartnn · Answer

you never solved a quadratic before ??

can you tell me 2 numbers whose sum is -2
and product is -8
?

anonymous · Answer

-4 and 2?

hartnn · Answer

correct!

so we split -2t as 
$\Large -4t+2t$

hartnn · Answer

$x^2-4t+2t -8 =0 $
factor out x from first 2 terms
and
2 from the last 2 terms

hartnn · Answer

$t(t-4) +2(t-4) =0$

hartnn · Answer

$(t-4)(t+2) = 0$

hartnn · Answer

t-4 = 0   or t+2 =0 

t=4 or t = -2

anonymous · Answer

I got it!!! :D
Thank you kind stranger!

hartnn · Answer

welcome ^_^
happy to help :)