Question

Use the fact that a/b over c/d = a/b divided by c/d to simplify the rational expression, stating any restrictions:

pic attached of problem, since it's hard to type out.

Answer 1

I know the answer is: (x+1)(x+5)/(x-3)(x divided by 4) with restrictions being x is not = to -5, -4, -3, 1, and 3..... but I have no clue how to get there or show my work.

Answer 2

That's one HUGE image! Not so very clear nevertheless, but I can read it anyway :)
\[\frac{ \frac{ a }{ b } }{ \frac{ c }{ d } }=\frac{ a }{ b }\cdot \frac{ d }{ c }\]is what can be done here.

So:\[\frac{ x^2-1 }{ x^2-3 }\cdot \frac{ x^2+8x+15 }{ x^2+3x-4 }\]Now you have to factor everything and cancel out the common factors....

Answer 3

TYPO: Make that first denominator: x²-9 !!

Answer 4

in the beginning it is a/b divided by d/c, but it looks like yous says a/b * d/c or am I reading yours wrong?

Answer 5

yours^

Answer 6

if you divide by a fraction, you can also multiply with the reciprocal, which makes things easier. That is what I meant with (a/b)/(c/d)=(a/b)*(d/c) = (ad)/(bc). Now there is one simple fraction left.

Reciprocal of c/d is d/c

Answer 7

ohhh ok. I forgot about that.

Answer 8

So can you factor everything, or do you need help with that?

Answer 9

I'm horrible at factoring. Still trying to work that out.

Answer 10

It's not that hard.

The easiest form is when you've got the difference of two squares: a²-b²
It can be factored as (a+b)(a-b).
Why? Just FOIL (a+b)(a-b):
First: a*a=a²
Outer: a*-b=-ab
Inner: b*a=ab
Last: b*-b=-b²

Add up: a²-ab+ab-b² = a²-b².

So remember: a²-b²=(a+b)(a-b).

It's easy, because squares are easily recognised:

x²-9=x²-3²=(x+3)(x-3) and so on...

Answer 11

Next, take x²+8x+15.

This can be factored as (x+ ...)(x+ ...)
Maybe it is better to write a and b on the dots: (x+a)(x+b).
Is it hard to find the numbers a and b? Some think it is!
This is because they don't know this:

a+b=8 (the number of x terms)
a*b=15 (the constant at the end)

If you realise it also must be easy, small numbers (otherwise you can't find them, they make these questions just right for you!), then first try the ab=15 part.

There are not many choices to end up with 15:
1x15=15
3x5=15 and that is all!

It is not 1 and 15, because their sum is 16 instead of 8, so it is 3 and 5 of course!

So: x²+8x+15=(x+3)(x+5).

And remember: to get better at this, don't tell yourself your horrible, but...practise!!!

Answer 12

I definitely need a lot of practice. :-) Algebra has always been a struggle for me. Thanks so much for explaining it. It;s starting to make sense. :-)

Answer 13

YW! Hope you'll see improvement!