Algebra Rational Expressions/

simplifying rational

100

Simplify:

(2a^2 +10a)/ (3a^2 + 15a)

2/3

 ( a cannot = 0,-5)

200

(x^2+x−6)/(x^2 +8x+15)

(x-2)/(x+5)

x cannot = -3,-5

300

(4x+20)/x^2 * (x^2+x)/(2x+10)

x cannot = 0, -5

(2(x+1))/x

400

(3x^2-13x-30)/(18x^2-50)

(x-6)/(2(3x-5))

x cannot equal +- 5/3

500

(8x^2-46x+45)/(4x^2-17x+5)

(2x-9)/(x-3)

x cannot = 3, 5/4

Multiplying and Dividing

100

(7x)/(2x-10) divide (x^2-6x)/(x^2-11x+30)

7/2

x cannot = 5, 0, 6

200

(6x^2+x-15)/(4x^2) divide (3x^2+5x)

(2x-3)/(4x^3)

 x cannot = 0 and -5/3

300

(x^2-3x)/(x-2) * (x^2+x-6)/x

x^2-9

 x cannot = 2 and 0

400

((3x^2+13x+4)/(4x^2-16))/((8x+32)/(4x+8))

(3x+1)/(8x-16)

 x cannot = -2,-4,2

500

(1/x+2/(x-1))/(5/(x-1)

 

(3x-1)/(5x)

x cannot = 0,1

addition and subtraction

100

(5x)/(x+3) + 15/(x+3)

5 

x cannot = -3

200

Find the LCM of the polynomials:

24x^2

and 

8x^2-16x

24x^2(x-2)

300

(x+4)/(x^2-4) - 15/(x-2)

(-14x-26)/((x+2)(x-2)

400

(x^2-5)/(x^2+5x-14) - (x+3)/(x+7)

(-x+1)/((x+7)(x-2)

 x cannot = -7 or 2

500

(x+2)/(x-4) + 2/x + (5x)/(3x-1)

(8x^3-9x^2-28x+8)/(x(x-4)(3x-1))

Equations

100

4/x + x = 5

x = 1 and 4

200

2/(3x) + 1/6 = 4/(3x)

x=4

300

(x-3)/(x+5) = x/(x+2)

x = -1

400

(x-1)/x + (2x-1)/(x+3) = (x+6)/ (x+3)

x = -

1/2

and 3

500

(3x)/(x+1) = 12/(x^2-1) + 2

x = -2 and 5

Inequalities

100

(x-5)/(x+3) >1

x<-3

200

(x^2-4x+8)/(x-1) < x

x<1 or x>8/3

300

6/(x-2)> -4

x<1/2 or x>2

400

(x+4)/4 > (x-2)/3

x<20

500

Factor:

12x^2+8xy-15y^2

(6x-5y)(2x+3y)