Question

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)

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

в)

$\displaystyle\frac4{x+4} ^{(\, (x-4)}-\frac x{x-4} ^{(\, (x+4)} =\frac{4x-16-(x^2 +4x)}{x^2 -4^2} =\\ \\ =\frac{4x-4x-x^2 -16}{x^2 -16} =\boxed{\displaystyle \frac{-x^2 -16}{x^2-16}}$

г)

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