algebra 2 questions...help me please?! :]

[alohadressageprincess]

Solve the fractions:

1. \(\displaystyle \L\\\frac{\frac{x^{3}-3x^{2}}{3x+6}}{\frac{x^{3}-8x^{2}+15x}{6x^{2}-18x-60}}\)



2. \(\displaystyle \L\\\frac{6x+5}{2x+6} - \frac{2x-7}{2x+6}\)


3. \(\displaystyle \L\\\frac{x}{2y} + \frac{5x}{y}\)



THANK YOU!!!!

 

[galactus]

Where seems to be your trouble?. The first one looks scary, but if you factor the quadratics and cancel it'll simplify quite nicely.

 

[alohadressageprincess]

to: galactus

ok, so all of these problems i have tried to teach myself how to do them with the instructions in my book, but i cant figure them out! :[

do i have to get them all so that they have a common denominator, then add like terms?

 

[jwpaine]

I'll help you on the first one.

I'll assume you mean this:
\(\displaystyle \L \frac{x^{3}-3x^{2}}{3x+6}\,/\,\frac{x^{3}-8x^{2}+15x}{6x^{2}-18x-60}\)

FACTOR:

=\(\displaystyle \L \frac{x^{2}(x-3)}{3(x+2)}\,/\, \frac{x(x-5)(x-3)}{6(x-5)(x+2)}\)

Change division to multiplication by the reciprocal:

=\(\displaystyle \L \frac{x^{2}(x-3)}{3(x+2)}\, \cdot \, \frac{6(x-5)(x+2)}{x(x-5)(x-3)}\)

Cancel out any common factors:


=\(\displaystyle \L \frac{x^{2}}{3}\, \cdot \, \frac{6}{x}\)

Multiple the fractions:

=\(\displaystyle \L \frac{6x^{2}}{3x}\)

Now simplify some more.....

 

[jonboy]

On number 2 you have like denominators so you can subtract.

Hence:\(\displaystyle \L \;\frac{6x\,+\,5}{2x\,+\,6}\,-\,\frac{2x\,-\,7}{2x\,+\,6}\,=\,\frac{6x\,+\,5\,-\,2x\,+\,14}{2x\,+\,6}\)

So simplify and then cancel anything that you can.

On number 3 get like denominators.

Multiply the "top" and "bottom" (denominator) of \(\displaystyle \frac{5x}{y}\) by \(\displaystyle 2\):\(\displaystyle \L \;\frac{x}{2y}\,+\,\frac{10x}{2y}\,=\,\frac{x\,+\,10x}{2y}\)

Once again, simplify and cancel anything you can.

 

[Mrspi]

On that first problem, you assisted with, Jonboy, you should have

(6x + 5) - (2x - 7)
---------------------
        2x + 6

or, 

6x + 5 - 2x + 7
------------------
    2x + 6

or

4x + 12
---------
2x + 6

4(x + 3)
---------
2(x + 3)

Now....reduce the fraction.