1)
22р⁴q² / 99p⁵q = 2q/9p
7a/(a²+5a) = 7a / [ a(a+5) ] = 7/(a+5)
(y²-z²) / (2y+2z) = [ (y-z)(y+z) ] / [ 2(y+z) ] = (y-z)/2 = 0.5 *(y-z)
(a²-1)/(a²-2a+1) = [ (a-1)(a+1) ] / (a-1)² = (a+1)/(a-1)
2)
(y-20)/4y - (5y - 2)/ y² =
= [ y(y-20) - 4(5y-2) ] / 4y² =
= [ y² -20y - 20y + 8 ] / 4y² =
= [y² - 40y + 8 ] / 4y²
1/(5c-d) - 1/(5c+d) =
= [ 1*(5c+d) - 1*(5c-d) ] / [ (5c+d)(5c-d) ]=
= [ 5c+d - 5c +d ] / [ (5c)² - d² ] =
= 2d / (25c² -d²)
7/(a+5) - [ (7a-3)/(a² +5a) ] =
=7/(a+5) - [ (7a-3)/ a(a+5) ] =
= [ 7a - (7a-3) ] / [ a(a+5) ] =
= [ 7a - 7a + 3 ] / [a(a+5) ] =
= 3/ [ a(a+5) ] = 3/(a² +5a)
3)
[ 1/(x+1) ] - [ 2/(x-2) ] + [ 3/(x²-1) ]=
= [ 1/(x+1) ] - [(2/ (x-2) ] + [3/ (x-1)(x+1) ] =
= [ 1*(x-1)(x-2) - 2(x-1)(x+1) + 3(x-2) ] / [ (x+1)(x-1)(x-2) ] =
= [ x²-2x -1x + 2 - 2(x²-1) + 3x +3*(-2) ] / [(x²-1)(x-2) ]=
= [ x² -3x + 2 -2x² + 2 +3x - 6 ] / [ (x² -1)(x-2) ] =
= [ (x² - 2x²) + (-3x+3x) + (2+2-6) ] / [ (x²-1)(x-2)]=
= [ -x² - 2 ] / [(x²-1)(x-2) ] =
= [ -(x²+2) ] / [ (x²-1)(x-2) ] =
= - [ (x+2)/ ((x²-1)(x-2)) ]