Rational Equations

Long Division

100

x^4 -3x³-7x-14÷(x-4)

x³+2x²+4x+23- 106/(x-4)

200

2x³-10x²+x-5÷(x-5)

2x²+1

300

(x²+x-42)÷(x+7)

(x-6)

400

3x^4-x³+5x-1÷(x+2)

3x³-7x²+14x-23+45/(x+2)

500

(x³+x²-x-2)÷(x+2)

x^{3 +} _x^{2 -x-2) / (x+2)}

Simplify

100

49a^3bc^4/35ab^5c

7a^2c^3/5b^4

200

x-3/x^3-27

x^2-9

300

2(x+5)/(x-5)(x-9)

2/(x-9)

400

32x^2y^5/8x^5y

y^4/4x^3

500

zx^5y/zx^5q

y➗q

Multiply

100

5x^3y times y^2 X^3y^2. 15x^2

Y^2/3x

200

(x-3)times(x²-4)/(x²-x-6)

(-3x²-4x+12)/(-4x²-3x+18)

300

(4/a^2)(a/8)

4a/8a^2

400

((a+3)/2)times((6)/3a+9)

=1

500

((x²-4)/(x²-1))times((x+1)/(x²+2x))

(x³+x²-4x-4)/(x^4+x²x)

Solving

100

(x²-64)/(x-8)=5

x=8  x=-3

200

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

x= -3

300

16/x²-16=2/x-4

x=4

400

5/x+2=4/x-2

x=18

500

-4/x+4=-3/x+6

x=12

Questions

100

What is a rational equation?

Mathematical sentence that establishes a equivalent relationship between two expressions

200

How to solve a rational equation?

1. Find common denominator

2. Multiply Everything by common denominator

3. Simplify

4.Check answers and for extraneous solutions

300

What kind of equation is rational?

an equation that contains fractions with xs in the numerator, denominator or both.

400

Whats an extraneous solution?

Values that we get when solving equations that aren't really solutions to the equation

500

What makes an equation no solution?

No solution means there is no value that can make the statement true