Help with simplifying rational functions to its lowest term

[Jessikaminshew]

Problem #1:

\(\displaystyle \frac{7z+8}{z-6}+\frac{9z+9}{z-6}\)


Problem #2:

\(\displaystyle \frac{(p+q)^{3}}{5p-5q}\cdot\frac{5p}{p^{2}+pq}\)

 

[Denis]

Re: Help with simplifying rational functions to its lowest t

Question number 1)                             Question number 2)
 7z+8   9z+9                                           (p+q)^3      5p
____ +_____                                           _______ X ______
z-6     z-6                                            5p-5q    p^2+pq

HINTS:
#1: a / x + b / x = (a+b) / x

#2: 5p-5q = 5(p-q) ; p^2+pq = p(p+q) ; and are you sure 5p-5q is not 5p+5q?

 

[galactus]

Re: Help with simplifying rational functions to its lowest t

Problem #1:

\(\displaystyle \frac{7z+8}{z-6}+\frac{9z+9}{z-6}\)

You do this like adding a regular ol' fraction. Notice the denominators are the same. That makes it easier.

How would you add \(\displaystyle \frac{3}{10}+\frac{7}{10}\)?. you would add across the top and get \(\displaystyle \frac{7+3}{10}=\frac{10}{10}=1\)

Same thing here. \(\displaystyle \frac{7z+8+9z+9}{z-6}\). Combine like terms in the top and you're done.

Problem #2:

\(\displaystyle \frac{(p+q)^{3}}{5p-5q}\cdot\frac{5p}{p^{2}+pq}\)

This is multiply. It's easier than add or subtract. Factor a 5 out of the left denominator and a p out of the right denominator.

Cancel terms and that's it.

 

[Jessikaminshew]

Re: Help with simplifying rational functions to its lowest t

HINTS:
#1: a / x + b / x = (a+b) / x

#2: 5p-5q = 5(p-q) ; p^2+pq = p(p+q) ; and are you sure 5p-5q is not 5p+5q?[/quote]


Yes, the denominator of the first sequence states: 5p-5q

 

[Jessikaminshew]

Re: Help with simplifying rational functions to its lowest t

Galactus, after factoring and canceling like terms, I'm left with p/p-q. I Have a feeling this is incorrect, can you elaborate?

 

[Jessikaminshew]

Re: Help with simplifying rational functions to its lowest t

Do I multiply the numerators and factor the denominators and then combine/cancel terms? Will that leave me the answer in simplest terms?

 

[mmm4444bot]

I'm left with p/p-q

The denominator is correct, but check your numerator.

You canceled the factor (p + q) in the denominator with something in the numerator, yes? Check your cancellation on top.

Also, don't text an algebraic fraction as "p/p-q" because the Order of Operations makes it simplify to "1 - q".

It is very important to text grouping symbols around such denominators, so text it this way: p/(p - q).

MY EDIT: Added comments about missing grouping symbols

 

[galactus]

Re: Help with simplifying rational functions to its lowest t

\(\displaystyle \frac{7z+8}{z-6}+\frac{9z+9}{z-6}\)

Sorry, I forgot how to add. After combining like terms, there is no factoring.

\(\displaystyle \frac{7z+8+9z-6}{z-6}\)

\(\displaystyle \frac{16z+17}{z-6}\)

That's it.

#2:

\(\displaystyle \frac{(p+q)^{\not{3}^{2}}}{\not{5}(p-q)}\cdot \frac{\not{5}\not{p}}{\not{p}(\not{p}\not{+}\not{q})}=\frac{(p+q)^{2}}{p-q}\)

 

[Denis]

Re: Help with simplifying rational functions to its lowest t

Sorry, I forgot how to add. After combining like terms, there is no factoring.

To the corner, Galactus...

 

[Deleted member 4993]

Re: Help with simplifying rational functions to its lowest t

Sorry, I forgot how to add. After combining like terms, there is no factoring.

To the corner, Galactus...

And he wrote 9z - 6 ....... doubletime.......