Вправи: 655

655. Спростіть вираз:

1) a+3\a+3a-3 – a-3\a-3a+3 = a+6a+9-(a-6a+9)(a-3)(a+3) = a+6a+9- a+6a-9a-9 = 12aa-9;

2) m+ p\m+pm- p + m-p\m-pp+m = m+2mp+ p+ m-2mp+ p(m- p)(m+ p) = 2m+2pm- p.

3) x+1\1+x1- x + x-1\1-xx+1 = x+2x+1+(x-1)(1- x)(1-x)(1+ x) = x+2x+1-(1-x) 21- x = x+2x+1-(1-2x+ x)1- x = x+2x+1-1+2x- x1- x = 4x1- x.

4) m+2n\m+2nm-2n – m+4nn-4n = (m+2n)2-(m+4n)(m-2n)(m+2n) = m+4mn+4n- m-4n m-4n = 4mnm-4n.