Rational Expressions & Equations 10/24

Simplify Rational Expressions

100

Simplify the expression

(16c^2b^4)/(8c^3b)

(2b^3)/(c)

200

Simplify the rational expression

(n+3)/(n^2+10n+21)

1/(n+7)

300

Simplify the rational expression

(x^2-2x-35)/(x^2-9x+14)

(x+5)/(x-2)

400

Simplify the rational expression

(4x^2-20x)/(x^2-4x-5)

(4x)/(x+1)

500

Simplify the rational expression

(x^3-x)/(x^3+8x-9x)

(x+1)/(x+9)

Multiply Rational Expressions

100

(2x^3)/(7x) * 14/x

4x

200

(12a^2c^3)/(21b) * (14b^2)/(6a^5b)

(4bc^2)/(3a^3)

300

(x^2 + 19x + 84)/(x^2 - 144) * (4)/(x+7)

4/(x-12)

400

(x^2+x-2)/(x+2) * (4x)/(x-1)

4x

500

(y^2-1)/(y^2-49) * (y-7)/(y+1)

(y-1)/(y+7)

Divide Rational Expressions

100

(4x^5)/y div (10x)/(2y^2)

(4x^4y)/5

200

(21ab^3)/(4c^2) div (7a^5)/(6a^2c^2)

(9b^3)/(2a^2)

300

(x^2+x-42)/3 ÷ (x^2 - 36)/(3x)

(x(x+7))/(x+6)

400

(n^2+7n+12)/(16n^2) div (n+3)/(2n)

(n+4)/(8n)

500

(x^2-36)/(2x^2+3x+1) div (4x-24)/(8x+4)

(x+6)/(x+1)

Add/Subtract Rational Expressions

100

Add the rational expressions. Simplify if possible.

(7y)/12+(3y)/4

(4y)/3

200

Add the rational expressions. Simplify if possible.

(7x - 2)/(6x) + (-3x + 1)/(x)

(-11x + 4)/(6x)

300

Subtract the rational expressions. Simplify if possible.

(2x^2+64)/(x^2-64) - (x-4)/(x+8)

(x+4)/(x-8)

400

Add the rational expressions. Simplify if possible.

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

5/(x-4)

500

Subtract the rational expressions. Simplify if possible.

(5x+11)/(x^2+5x+6) - 4/(x+3)

1/(x+2)

Solving Rational Equations/Inequalities

100

Solve the  equation:

x/4 - (x-1)/6 < 5/12

x < 3

200

State restrictions. Solve the equation:

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

x=6

300

State the restrictions. Solve the equation. Check for extraneous solutions:

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

x=2,3

400

State Restrictions. Solve for x. Check for extraneous solutions:

1/(x-2) + 1/(x+2) = 4/(x^2-4)

no solution

500

Solve the equation:

x^2/6 + (x-2)/4 > (x+1)/3

( neg. infinity,-2) u (2, infinity)