Simplify completely quantity x squared plus 4 x minus 5 over quantity 5 x squared minus 8 x plus 3 times quantity 20 x minus 12 over x squared minus 6 x minus 55 how do I simplify this?

Question

campbell_st · Answer

well you have 

$$\frac{x^2 +4x - 5}{5x^2 -8x + 3} \times \frac{20x - 12}{x^2 -6x - 55}$$

start by doing some factoring

$$\frac{(x + 5)(x -1)}{(x -1)(5x - 3)} \times \frac{4(5x -3)}{(x - 11)(x + 5)}$$

cancel common factors and then see whats left...

sarahezzmck · Answer

So you cancel (x+5) and 4(5x-3)?

campbell_st · Answer

and you can also cancel (x -1) 

so whats left...?

campbell_st · Answer

the 4 won't cancel... just (5x -3)

sarahezzmck · Answer

Yes, I caught that, I apologize. So the remanders are 4/(x-11)?

sarahezzmck · Answer

So the answer is 4/x-11!! OMG thank you :)

campbell_st · Answer

yep... thats it... all with a little factoring.

sarahezzmck · Answer

Quick question, idk If you know how to answer this but what happens when you have a remainder?

campbell_st · Answer

nothing.... its just just expressed as a fraction  4/(x -11)

its not really a remainder... the the result of multiplying 2 fractions...

sarahezzmck · Answer

I mean, I have a DBA in a couple of minutes, the question that I have to answer is "What happens when you have a remainder?" and I don't exactly know what happens and that might sound stupid and I'm really sorry but that's the question...

campbell_st · Answer

so 10 divided by 7 is 1 and remainder 3     so the remainder tells you its just 3 sevenths of  the whole.... that left...     

its always written over the divisor of 7... 

hope that helps

sarahezzmck · Answer

so when there is a remainder it basically just turns into a fraction?

campbell_st · Answer

yes thats it

sarahezzmck · Answer

Thank you! Could you help me for like two more questions please?

campbell_st · Answer

I can do 1 I'm have to go in about 10 mins

sarahezzmck · Answer

What is the restriction on the quotient of quantity 5 x squared minus 10 x minus 15 divided by quantity x squared minus 9 divided by quantity 6 x plus 12 divided by quantity x plus 2

campbell_st · Answer

ok.. so the problem is 

$$\frac{5x^2 -10x -15}{x^2 - 9} \div \frac{6x + 12}{x + 2}$$

so a little factoring and you get 

remember dividing by a fraction, flip and multiply



$$\frac{5(x - 3)(x + 1)}{(x -3)(x + 3} \times \frac{(x + 2)}{6(x + 2)}$$

cancelling common factors you have 

$$\frac{5(x +1)}{6(x + 3)}$$

so the restriction appears to be x cannor by -3... which gives a zero denominator, which is undefined...

not sure if that was what you ment..

sarahezzmck · Answer

It was the first one, and I'm so sorry I was doing my DBA.