least common denominator?

Question

________ ______
(a^2-7a+6) (a^2-36)

this is hard.how would i find the least common denominator.
is there a online calculator of something that can help me.because i have alot of these to do to get a passing grade.?
im not a math genius so please dont tell me this is easy.please
let me know if you know about a website similar to quickmath.com to help me with these type of problems

Answer 1

Assuming it is two expressions ADDED together:-
[1 / (a - 6) (a - 1) ] + [1 / (a - 6) (a + 6) ]
[ (a + 6) + (a - 1)] / [(a - 6) (a - 1) (a + 6)]
[ 2a + 5 ] / [ (a - 6) (a - 1) (a + 6) ]

Answer 2

Hi! Don't panic, just go one step at a time. You can do this.

To find the least common denominator, you're going to need to factorize, that is to say find the factors, of the two fractions.

The first parenthesis is:
aˆ2 - 7a + 6
this is a quadratic equation. to find its factors you need to:
1-find the factors of 6: 1*6, 2*3
consider which of these two sets could give you the -7 that multiplies a: well, -1 times -6 is 6, and -1-6 is -7

so the factors of that equation are:(a-1)(a-6)
[multiply it out and you'll see you get aˆ2 - 7a + 6]

now the second one is a little trickier and this is how you see if you've studied.

aˆ2-36 is a difference of squares; that is to say, it's a square minus another square. don't see it? think of it this way:

aˆ2 - 6ˆ2 (because 6*6 is 36, right?)

equations that are a difference of squares have a simple way of being solved. this is the basic formula:

xˆ2 - yˆ2 = (x + y)(x-y)
[multiply it out, you'll see it works]

so here:
aˆ2 - 6ˆ2 = (a+6)(a-6)

now in the first case you had factors: (a-1)(a-6)
and in the second case you had factors: (a+6)(a-6)

you can see that they have (a-6) in common, so it doesn't need to be repeated.

the least common denominator, then, is: (a-6)(a-1)(a+6)

Answer 3

You need to factorise the two bracketed expressions.
a^2 - 36 is the difference of two squares: a^2 - 6^2.
That factorises to (a - 6)(a + 6).
The difference of two squares a^2 - b^2 always factorises to:
(a + b)(a - b).

For a^2 - 7a + 6, you need to find two numbers which multiply to give 6 and add to give -7. Because the 7 is negative and the 6 positive, that means both numbers must be negative.

6 can be factorised as 2 * 3 or 6 * 1.
Only the second pair adds up to 7.
The factors are therefore (a - 6)(a - 1).

The common denominator is therefore (a - 6)(a - 1)(a + 6).

Answer 4

I'm not going to claim this is easy, BUT, you do have to learn how to do it in order to pass. Thus a "quick calculator" won't help. To find the least common denominator, you first have to factor the two polynomials.

The first one factors into (a-1)(a-6).

The second factors into (a-6)(a+6).

Then you look at how many different terms you have. Here you have three. (a-1)(a-6)(a+6). You only count each term once. Then you multiply them together to get your LCD. However, most math teachers won't make you multiply it all back out. You can just write it down as "(a-1)(a+6)(a-6)".

Answer 5

it's not easy when you don't know where to begin, but it's not that bad once you know how to start off. 1st, you need to factor each part in the (). let's take a look at a^2-7a+6; that factors into (a-6)(a-1). now factoring a^2-36, you can see that's the same as (a-6)(a+6). you notice that (a-6) is in both? that's your answer. good luck with the rest of your problems