What is the least common denominator of the rational expressions below? 1/x^2-5x+3/x^2+2x-35

Here the denominators are quadratics , so we need to factorise them first

1/(x²-5x) +3/(x²+2x-35)

factorising x²-5x ,

here GCF is x, so taking x out we have

x(x-5)

factorising x²+2x-35 using AC method,

we find factors of -35 that add up to give 2

(x-5)(x+7)

Since we have x-5 common in both denominators, so lcd of the rational expression will be product of x(x-5)(x+7)

lcd is x(x-5)(x+7)

it would rotate about 180 degrees.