Упростите выражение: а) x/(y−1) + 5/(1−y); б) a/(c−3) − 6/(3−c); в) 2m/(m−n) + 2n/(n−m); г) 5p/(2q−p) + 10q/(p−2q); д) (a²+16)/(a−4) + 8a/(4−a); е) (x²+9y²)/(x−3y) + 6xy/(3y−x).

а) \(\dfrac{x}{y-1}-\dfrac{5}{y-1}=\dfrac{x-5}{y-1}\).

б) \(\dfrac{a}{c-3}+\dfrac{6}{c-3}=\dfrac{a+6}{c-3}\).

в) \(\dfrac{2m}{m-n}-\dfrac{2n}{m-n}=\dfrac{2(m-n)}{m-n}=2\).

г) \(\dfrac{5p}{2q-p}-\dfrac{10q}{2q-p}=\dfrac{5(p-2q)}{2q-p}=-5\).

д) \(\dfrac{a^2+16}{a-4}-\dfrac{8a}{a-4}=\dfrac{a^2-8a+16}{a-4}=\dfrac{(a-4)^2}{a-4}=a-4\).

е) \(\dfrac{x^2+9y^2}{x-3y}-\dfrac{6xy}{x-3y}=\dfrac{(x-3y)^2}{x-3y}=x-3y\).