Сокращение алгебраических дробей Номер 1
1. 3x-15y/4x-20
2. 4-2a/6a-12
3. a^2+3a/15+5a
4. 16x+8y/9y+18x
5. x^2-4x/28-7x
6. 18y^2-9y/3y^2-6y^3
7. 7x-14y/21(2y-x)
8. 2(x-b)/3(b-x)
9. 3x+9/15(x+3)
10. 5-x/x-5
Номер 2
1. 2a+18/a^2+18a+81
2. x^2-10x+25/5x-25
3. x^2+8x+16/4x+16
4. a^2-10a+25/-4a+20
5. y^2+8y+16/2y+8
6. x^2-4y^2/x^2+4xy+4y^2
7. 9y^2+24y+16/9y^2-16
8. x^2-4x+4/3x-6
9. 6x^2+36x+54/(-3x-9)^2
10. 15x-9y/25x^2-30xy+9y^2
Номер 3
1. x^7+x^5/x^7+x^9
2. y^6+y^4/y^6+y^8
3. a^2+a^5/a^8+a^5
4. (x-y)^2/x(x^2-2xy+y^2)
5. 14a^2(x-y)^2/21a(x^2-y^2)
6. -ax-yx/by+ba
7. x^3-3x^2-2x+6/x^3-27
8. x^3+8/x^3+2x^2-3x-6
9. x^3-2x^2-3x+6/x^3-8
10. x^3+27/x^3+3x^2-2x-6
Номер 4
1. -a^2/a^2
2. 8x^7y(a+b)/22x^13y^3(a+b)
3. 2a(b+c)/4a^3(b+c)(b-c)
4. 6(x-y)/12z(y-x)
5. (x+8)^5/(x+8)^2
6. 4x^2-9/9-12x+4x^2
7. a^2-2a/a^2-4
8. (3a-3c)^2/9c^2-9a^2
9. 2b(m+n)/6bc(m+n)
10. x^2-y^2/x(x+y)
11. 20+10a+5a^2/a^3-8
Решите
1) √3/ 3-x² < 2/ √3-x
2/(√3-x)-√3/(√3-x)(√3+x)>0
(2√3+2x-√3)/(√3-x)(√3+x)>0
(2x+√3)/(√3-x)(√3+x)>0
x=-√3/2 x=√3 x=-√3
+ _ + _
(-√3)[-√3/2](√3)
x∈(-∞;-√3) U [-√3/2;√3)
2)3/ x²-1 - 1/2 < 3/ 2x-2
3/2(x-1)-3/(x-1)(x+1)+1/2>0
(3x+3-6+x²-1)/2(x-1)(x+1)>0
(x²+3x-4)/2(x-1)(x+1)>0
x²+3x-4=0⇒x1+x2=-3 U x1*x2=-4⇒x1=-4 U x2=1
(x+4)(x-1)/2(x-1)(x+1)>0
(x+4)/2(x+1)>0
x=-4 x=-1
+ _ + _
(-4)(-1)(1)
x∈(-∞-4) U (-1;1) U (1;∞)
x²=a
4a²+a-3=0
D=1+48=49
a1=(-1-7)/8=-1 ⇒x²=-1 U a2=(-1+7)/8=0,75⇒x²=3/4⇒x=-√3/2 U x=√3/2
x1+x2=-5 U x1*x2=6⇒x1=-3 U x2=-2
+ _ + _ +
(-3)(-2)[-√3/2][√3/2]
x∈(-3;-2) U [-√3/2;√3/2]
2)(x⁴-2x²-8)/ (x⁴-2x²-3) > 0
x²=a
a²-2a-8=0
a1=a2=2 U a1*a2=-8
a1=-2⇒x²=-2 U a2=4⇒x²=4⇒x=-2 U x=2
x²=b
b²-2b-3=0
b1=b2=2 U b1*b2=-3
b1=-1⇒x²=-1 U b2=3⇒x=-√3 U x=√3
+ _ + _ +
(-2)(-√3)(√3)(2)
x∈(-∞;-2) U (-√3;√3) U (2;∞)