1) a/16 + x/16 =(a+x)/16
2) 5m/n - 3m/n =2m/n
3) 3x +4y/12 - x+2y/12 =2x+6y/12=2x+y/2
4) a+2b/2c - a-4b/2c =b/c-2b/c=-b/c
5) a-8/a^2-25 + 13/a^2-25 =a-8/(a+5)*(a-5)
6) 5x+1/2 - x/2 =9x/2+1/2=4,5x+1/2
7) a+3/4 - a+1/4 =4/4=1
8) 2x/a-b - x/b-a =2x/a-b + x/a-b=3x/a-b
9) a/x-1 + b/1-x =a/x-1 - b/x-1=a-b/x-1
10) a-5/a-3 + a+5/3-a =a-5/a-3 - a+5/a-3=(a-5)*(a+5)/a-3=(a^2-25)/a-3
11) 3x-2/5 + 5x-3/3 =(9x-6+25x-15)/15=(24x-21)/15=3*(8x-7)/15=(8x-7)/5
12) 2m+5/6 - m-a/8 =m+(20-6a)/24=m+2*(10-3a)/24=m+(10-3a)/12
13) 7/10a -5/4a =(70-25)/20a=45/20a=9/4a
2x²-3x-2=0
D=9-4*2*(-2)=9+16=25
x₁=3-5=-1/2
4
x₂=3+5=2
4
2) 3x²+8x-3=3(x-1/3)(x+3)=(3x-1)(x+3)
3x²+8x-3=0
D=64-4*3*(-3)=64+36=100
x₁=-8-10=-3
6
x₂=-8+10=1/3
6
3) 3x²+2x-1=3(x-1/3)(x+1)=(3x-1)(x+1)
3x²+2x-1=0
D=4+12=16
x₁=-2-4=-1
6
x₂=-2+4=1/3
6
4) 2x²+5x-3=2(x-1/2)(x+3)=(2x-1)(x+3)
2x²+5x-3=0
D=25+4*2*3=25+24=49
x₁=-5-7=-3
4
x₂=-5+7=1/2
4
5) x²-x-30=(x+5)(x-6)
x²-x-30=0
D=1+120=121
x₁=1-11=-5
2
x₂=1+11=6
2
6) x²+x-42=(x+7)(x-6)
x²+x-42=0
D=1+168=169
x₁=-1-13=-7
2
x₂=-1+13=6
2
7) 2x²+7x-4=2(x-1/2)(x+4)=(2x-1)(x+4)
2x²+7x-4=0
D=49+32=81
x₁=-7-9=-4
4
x₂=-7+9=1/2
4
8) 5x²-3x-2=5(x+2/5)(x-1)=(5x+2)(x-1)
5x²-3x-2=0
D=9+40=49
x₁=3-7= -4/10=-2/5
10
x₂=3+7=1
10
9) 3x²+5x+2=3(x+2/3)(x+1)=(3x+2)(x+1)
3x²+5x+2=0
D=25-24=1
x₁=-5-1=-1
6
x₂=-5+1=-2/3
6
10) 2x²-7x+6=2(x-3/2)(x-2)=(2x-3)(x-2)
2x²-7x+6=0
D=49-48=1
x₁=7-1=6/4=3/2
4
x₂=7+1=2
4
1) a/16 + x/16 =(a+x)/16
2) 5m/n - 3m/n =2m/n
3) 3x +4y/12 - x+2y/12 =2x+6y/12=2x+y/2
4) a+2b/2c - a-4b/2c =b/c-2b/c=-b/c
5) a-8/a^2-25 + 13/a^2-25 =a-8/(a+5)*(a-5)
6) 5x+1/2 - x/2 =9x/2+1/2=4,5x+1/2
7) a+3/4 - a+1/4 =4/4=1
8) 2x/a-b - x/b-a =2x/a-b + x/a-b=3x/a-b
9) a/x-1 + b/1-x =a/x-1 - b/x-1=a-b/x-1
10) a-5/a-3 + a+5/3-a =a-5/a-3 - a+5/a-3=(a-5)*(a+5)/a-3=(a^2-25)/a-3
11) 3x-2/5 + 5x-3/3 =(9x-6+25x-15)/15=(24x-21)/15=3*(8x-7)/15=(8x-7)/5
12) 2m+5/6 - m-a/8 =m+(20-6a)/24=m+2*(10-3a)/24=m+(10-3a)/12
13) 7/10a -5/4a =(70-25)/20a=45/20a=9/4a