Polynomials

May 2010
24
0
For the following rational expressions, perform the indicated operation and simplify the result:

a) y³-1 y-1
__________ ______
y² + y - 6 divided by 3+y




b) are there any restrictions on the variable y?


Hey guys i need help on how to do this, i have no idea where to start (Worried)
 
May 2010
24
0
For the following rational expressions, perform the indicated operation and simplify the result:

a) y³-1 y-1
__________ ______
y² + y - 6 divided by 3+y




b) are there any restrictions on the variable y?


Hey guys i need help on how to do this, i have no idea where to start (Worried)
its y-1 / 3+y
 

masters

MHF Helper
Jan 2008
2,550
1,187
Big Stone Gap, Virginia
For the following rational expressions, perform the indicated operation and simplify the result:

a) y³-1 y-1
__________ ______
y² + y - 6 divided by 3+y


b) are there any restrictions on the variable y?

Hey guys i need help on how to do this, i have no idea where to start (Worried)
Hi Cockchestner007,

I'm having a wee bit of trouble untangling what you have.
Is it this?

\(\displaystyle \frac{y^3-1}{y^2+y-6} \div \frac{y-1}{3+y}\)

If not, you might want to use grouping symbols to show exactly what you have.
 

masters

MHF Helper
Jan 2008
2,550
1,187
Big Stone Gap, Virginia
Hi Cockchestner007,


\(\displaystyle \frac{y^3-1}{y^2+y-6} \div \frac{y-1}{3+y}\)

Invert the divisor and multiply.

\(\displaystyle \frac{y^3-1}{y^2+y-6} \cdot \frac{y+3}{y-1}\)

\(\displaystyle \frac{(y-1)(y^2+y+1)}{(y+3)(y-2)} \cdot \frac{y+3}{y-1}\)

The "restrictions of the variable" means "what would y have to be to make the denominator of either fraction zero?"

Those restrictions would be: y cannot be -3, 2, or 1
Simplifying we arrive at:

\(\displaystyle \frac{y^2+y+1}{y-2}\)

The only restriction after simplification is y cannot be 2.
If we were talking about rational functions, this would be a vertical asymptote.

The other two restrictions would be points of discontinuity on the graph.

But, this may be too much information since these are only expressions.