1) 5x²/(x-1) - 5x·(x-1)/(x-1) = (5x²- 5x)/(x-1) = 5x(x-1)/(x-1) = 5x
2) [4m² - 4m(3-m)]/(3-m) = (4m² - 12m +4m²)/(3-m) = 4m(m-3)/(3-m) = -4m
3) 8n/(2-n) -4n = 4n·(2-2+n)/(2-n) = 4n²/(2-n)
4) [3a·(2a+5) - 6a²]/(2a+5) = 15a/(2a+5
5) [12b - 2b·(6-b)]/(6-b) = 2b²/(6-b)
6) [14a - 7a·(2-a)]/(2-a) = 7a²/(2-a)
1) (a+3)/(a-1) - (a+5)/2(a-1) = [2(a+3) -(a+5)]/2(a-1) = (a -1)/2(a-1) =1/2 = 0,5
2) 4m/(m²-n²) - (m-n)/(m²-n²) = (4m -(m-n))/(m²-n²) = (3m+4n)/(m²-n²)
3) [2·(2x-y) +y]/(4x+2y) = (4x-y)/(4x+2y)
4) (x²+y²)/(x²-y²) - (x-y)²/(x²-y²) = (x²+y² -x²+2xy -y²)/(x²-y²)= 2xy/(x²-y²)
5) 4/(a²-3²) +/- 2/a(a+2) = [4a +/-2(a-3))/a(a²-9)
pri + = (6a -6)/a(a²-9) = 6(a-1)/a(a²-9)
pri - = (2a +6)/a(a²-9) = 2(a+3)/a(a+3)(a-3) = 2/a(a-3)
6) 1/2(m-2) -m/(m²-4) = (m+2-m)/(m²-4) = 2/(m²-4)
7) 4(x²+1)/[(4x+3)(4x-3)] - (x²-1)/x(4x-3) = [4x(x²+1) - (x²-1)(4x+3)]/x(4x+3)(4x-3) =
= (4x³+4x -4x³-3x² +4x+3)/x(16x²-9) = (8x -3x² +3)/(16x³-9x)
8) b/(3b-1) + (1-3b²)/(3b-1)(3b+1) = [b(3b+1) +(1-3b²)]/ (9b²-1)=
=(3b² +b +1-3b²)/(9b²-1) =(b+1)/(9b²-1)
1) x²+10x+25 -x² = x-2
9x= -27
x= -3
2) 36-12x+x² -16 =x² -2x
20= -2x+12x = 10x
x=2
3) [(3x+1)+(3x-1)]·[(3x+1)-(3x-1)] = x+5
6x·2 =x+5
11x = 5
x= 5/11
4) [(2y-1)+(2y+1)]·[((2y-1)² - (2y-1)(2y+1) +(2y+1)²] = y+16y³+2
4y·(4y²-4y+1 -4y²+1 +4y² +4y+1) = 16y³ +y+1
4y·(4y²+3)=16y³+y+2
16y³ +12y = 16y³+y+2
11y=2
y=2/11