Rational equations

Knowledge needed: factoring

What does it mean for a fraction to be undefined?

For a fraction to be undefined the denominator has to be zero.

Simplfy 1+4/4+1

Simplfy 8+X/X+4

2

Simplify x-4/x-4

1

Simplify x-7/7-x

-1

Simplify 5-1/1-5

-1

What value of x would make the expression x/x+5 undefined?

-5

Write 5 as an equivalent fraction with a denominator of 2

10/2

Are rational expressions improper or proper

improper

how would you factor x²-4 ?

(x-2)(x+2)

-2×2=-4

When factoring, the numbers you get must ____ the factored number when _____ together.

equal, multiplied.

Factor 3x-9

3 is a multiple of 9

3(x-3)

Simplify x²-4/x+2

x-2

Simplify 3x-9/x²-3x

3/x

Rewrite the expression in reduced form: x²-49/7-x

-(x+7)

Rewrite the expression in simplest form then determine what value(s) make the expression undefined.

4- x-3/x+5

3x+23/x+5

-5

Simplify the following expression: x²-3x-18/x-6. Where would function be undefined?

(x+3)

Function is undefined at 6 because 6 - 6 = 0 (When it is divided by 0 it becomes undefined.

x/x+2 - 5 = - 2/x+2

No solution

1/x-1 + 1=- 7x/x-1

x=0

x - 2x/x+6 = 5/x+6

x= 1

x= -5

When you have a negative fraction and you simplify it, you have to change the __ ___ on the numerator to a ____ ___. Remember that there is a invisible 1 that turns negative.

Plus sign, negative sign

x - 3x+1/x+9 = 3

x=4

x=-7

SKIP

SKIP

Once you have the required equation (ax²+bx+c) you can use the ____ ____ or ____

Quadratic formula, factor

Remeber, you have have to make all ____ the same. Once they are the same you can _____ ___ ___

denominators the same. cancel them out

What ever you multiply the ____ by, multiple the ___ by.

bottom/denominator, top/numerator.

1/x²-x - x/x-1 = -3

x= 1/2