# Thread: Rational Expressions! = /

1. ## Rational Expressions! = /

Rational expressions....ok clueless. im not sure what steps to follow thru with.

Directions: Simplify each rational expression. State any restirctions on variable.

3y² - 3
y² - 1 ------> On problems like these, aren't you suppose to cross out like factors?

Or do you just do that on problems like these:

x² + 13x + 40
x² - 2x - 35 ----> do you find like factors (ex. what multiplies to give you 35, and add/subtracts to give you 2? uggh i dont know!

if that is then in this problem i think im heading the right way:

6x² + 5x - 6
= (x+6)(x-1)
3x² - 5x +2 uhmm....still working on it...tehehe.

can somebody please help me understand what are restrictions, how do you find them, and how do you simplify a rational expression?

Please and thank you!! = )

2. Originally Posted by topaz192
Rational expressions....ok clueless. im not sure what steps to follow thru with.

Directions: Simplify each rational expression. State any restirctions on variable.

3y² - 3
y² - 1 ------> On problems like these, aren't you suppose to cross out like factors?

Or do you just do that on problems like these:

x² + 13x + 40
x² - 2x - 35 ----> do you find like factors (ex. what multiplies to give you 35, and add/subtracts to give you 2? uggh i dont know!

if that is then in this problem i think im heading the right way:

6x² + 5x - 6
= (x+6)(x-1)
3x² - 5x +2 uhmm....still working on it...tehehe.

can somebody please help me understand what are restrictions, how do you find them, and how do you simplify a rational expression?

Please and thank you!! = )

All of them are rational expressions...

You are right on the money in that you need to factor and reduce.

$\displaystyle \frac{3y^2-3}{y^2-1}=\frac{3(y^2-1)}{y^2-1}=3$

by reducing out like terms.

As for the restrictions set the denominator equal to zero BEFORE you reduce the rational expression. Any of the zeros are not in the domain of the function.

example

$\displaystyle y^2-1=0$ factoring

$\displaystyle (y-1)(y+1)=0$

so y cannot equal plus or minus 1.

Good luck.

3. ok i got the first one. so a restriction is what it can not equal?

6x² + 5x - 6
3x² - 5x +2

so on one like this when reducing and factoring like terms itll be:

2x + 3
x - 1

and x cannot equal 1 or 2/3?

4. Originally Posted by topaz192
ok i got the first one. so a restriction is what it can not equal?

6x² + 5x - 6
3x² - 5x +2

so on one like this when reducing and factoring like terms itll be:

2x + 3
x - 1

and x cannot equal 1 or 2/3?

X only cannot equal 1. The reason being if you evaluate the expression for the value x=1. You would end up with zero in the denominator. Since division by zero is undefined, x cannot be 1.

zero in the numerator is okay. So negative 2/3 is fine.

5. Yay! lol thank you! = )