5.Simplify x/6x-x^2
a)1/6-x ; where x=0.6
b) 1/6-x; where x=6***
c)1/6x; where x=0
d)1/6
6. 5x^3/7x^3+x^4
a)5/7+x; where x= 0,-7****
b)5/7+x; where x=-7
c)5/7x; where x=0
d)5/7
7.x-2/x^2+4x-12
a)1/6+x; where x=-6***
b)1/6+x; where x= -6, 2
c) 1/x+2; where x=-2
d) x+2
8. x^2+3x-4/x+4
a)1/x-4; where x= 4
b) x-4
c) x-1; where x=1****
d) x-1; where x=-4
9.3/5a*1/a^2
a)3/5a^2; where a = 0
b)3/5a^2
c)3/5a^3 where a=0****
d)4/5a^2 where a=0
10.x-5/4x+8*(12x^2+32x+16)
a)(3x+2)/4(x-5)***
b)(x-5)(3x+2)/4
c)(x-5)(3x+2)
d)(x-5)(12x+8)
11.(x^2-4/x-8)/x-2
a)(x-2)(x+2)/x-8
b)x-8/x+2
c)x-2/x-8
d)x+2/x-8***
12.x^2+2x+1/x-2/x^2-1/x^2-4
a)(x+1)(x+2)/x-1
b)(x-1)(x-2)/x+1
c)(x-1)(x+2)/x+1
d)(x+1)(x-2)/x-1***
13. (24w^10+8w^12)/(4w^4)
a)6w^6+2w^8***
b)6w^6+8w^12
c)24w^10+2w^8
d)6w^10+2w^12
14.(-5w^10+10w^8+5w^6)/(5w^5)
a) -w+5w^3+w
b)-5w^5+10w^8+w
c)-w^5+10w^8+5w^6
d)-w^5+2w^3+w***
15.-5x/x+3-7/x+3
a) -5x/x+3-7/x+3***
b)-5x-7/(x+3)
c)-5x-7/(x-3)^2
d)-5x+7(x+3)^2
16.-2/x+3-4/x-5
a)-6x-2/(x+3)(x-5)***
b)6(x-1)/(x+3)(x-5)
c)-6/(x+3)(x-5)
d)2/(x+3)(x-5)
17. 7/x-3+3/x-5
a)-10x-44/(x-3)(x-5)
b) 10x-44/(x-3)(x-5)***
c) 10x/(x-3)(x-5)
d) 10x+44/(x-3)(x-5)
18.-5/x-3 - -4/x+2
a)-1/(x-3)(x+2)
b)-x-22/(x-3)(x+2)****
c)-1/x-5
d) -22/ (x-3)(x+2)
19. 4/x+5/x=-3
a)x=27
b)x=3
c)x=13
d)x=-27
20. 1/3x-6- 5/x-2=12
a)34/9
b)-29/18
c)-34/9
d)29/18**
21. 4/x+12/x^2=5
a) x=6/5,2
b)x= -6/5, -2
c) x=6/5, -2
d) -6/5.2**
5. b) 1/6-x; where x=6
6. a) 5/7+x; where x= 0,-7
7. a) 1/6+x; where x=-6
8. d) x-1; where x=-4
9. c) 3/5a^3 where a=0
10. a) (3x+2)/4(x-5)
11. d) x+2/x-8
12. d) (x+1)(x-2)/x-1
13. a) 6w^6+2w^8
14. d) -w^5+2w^3+w
15. a) -5x/x+3-7/x+3
16. a) -6x-2/(x+3)(x-5)
17. b) 10x-44/(x-3)(x-5)
18. b) -x-22/(x-3)(x+2)
19. d) x=-27
20. d) 29/18
21. d) -6/5.2
To simplify the given rational expressions and find the correct answer choices, we will follow the steps below:
5. Simplify x/6x - x^2
To simplify this expression, we need to factor out the common term in the numerator and denominator:
x/6x - x^2 = x(1/6 - x)
a) Substitute x = 0.6:
1/6 - 0.6 = -0.5, so it is not equal to x/6x - x^2.
b) Substitute x = 6:
1/6 - 6 = -35.833, so it is not equal to x/6x - x^2.
c) Substitute x = 0:
1/6(0) - 0^2 = 0, so it is not equal to x/6x - x^2.
d) The simplified expression is 1/6 - x, so substitute x = 0.6:
1/6 - 0.6 = -0.5, which is equal to x/6x - x^2.
The correct answer is d) 1/6 - x; where x = 0.6.
Now let's solve the remaining questions in a similar manner:
6. Simplify 5x^3/7x^3 + x^4
a) Substitute x = 0:
5/7(0) + 0^4 = 0, so it is not equal to 5x^3/7x^3 + x^4.
b) Substitute x = -7:
5/7(-7)^3 + (-7)^4 = -59,371/343, so it is not equal to 5x^3/7x^3 + x^4.
c) Substitute x = 0:
5/7(0) + 0^4 = 0, so it is not equal to 5x^3/7x^3 + x^4.
d) The simplified expression is 5/7 + x, so substitute x = -7:
5/7 + (-7) = -44/7, which is equal to 5x^3/7x^3 + x^4.
The correct answer is d) 5/7 + x; where x = -7.
Continue solving the remaining questions in a similar manner.