Question

Упростите выражение: а) y+ 3y/y-3 б) 2/x-5 + x+5/5x в) 4/x+4 - x/x-4 г) 2p-q/p2+qp + p-2q/pq+q2

Answer 1

а)

$displaystyle y+frac{3y}{y-3} =frac{y(y-3)}{y-3}+frac{3y}{y-3} =frac{y^2 -3y+3y}{y-3} =\ \ =boxed{displaystyle frac{y^2 }{y-3} }$

б)

$displaystyle frac2{x-5} ^{(5x}+frac {x+5}{5x} ^{(, (x-5)} =frac{2cdot 5x+x^2-5^2}{5x(x-5)} =\ \ =boxed{displaystyle frac{x^2+10x-25}{5x^2-25x}}$

в)

$displaystylefrac4{x+4} ^{(, (x-4)}-frac x{x-4} ^{(, (x+4)} =frac{4x-16-(x^2 +4x)}{x^2 -4^2} =\ \ =frac{4x-4x-x^2 -16}{x^2 -16} =boxed{displaystyle frac{-x^2 -16}{x^2-16}}$

г)

$displaystyle frac{2p-q}{p^2 +qp} +frac{p-2q}{pq+q^2} =frac{2p-q}{p(p+q)} ^{(q} +frac{p-2q}{q(p+q)} ^{(p} =\ \ =frac{2pq-q^2+p^2-2pq}{pq(p+q)} =frac{p^2-q^2}{pq(p+q)} =\ \ =frac{(p-q)(p+q)}{pq(p+q)} =boxed{displaystyle frac{p-q}{pq}}$