How do you simplify #(2t)/(s^2 - st) + (s+t)/(t^2 - s^2)#?
1 Answer
Explanation:
Your starting expression looks like this
#(2t)/(s^2 - st) + (s + t)/(t^2 - s^2)#
Notice that you can write
#s^2 - st = - (st - s^2)#
The expression becomes
#-(2t)/(st - s^2) + (s + t)/(t^2 - s^2)#
Now focus on factoring the two denominators. For
#st - s^2 = s * (t - s)#
Notice that the second denominator is a difference of squares, which means that you can factor it using
#color(blue)(a^2 - b^2 = (a-b)(a+b))#
In your case, you would have
#t^2 - s^2 = (t-s)(t+s)#
The expression can thus be written as
#-(2t)/(s(t-s)) + color(red)(cancel(color(black)((t+s))))/((t-s) color(red)(cancel(color(black)((t+s)))))#
#-(2t)/(s(t-s)) + 1/(t-s)#
Multiply the second fraction by
#-(2t)/(s(t-s)) + s/(s(t-s)) = color(green)((s - 2t)/(s(t-s))#