how do u multiply these...?

Question

3x-12/x+5 X x+6/2x-8 and
4(x+5)/x^2 X x(x+1)/2(x+5)

then i have to simplify the results but i dont know how to any of it please help!!

Answer 1

this is a very easy problem which they have twisted to make it look complex.reLax!!
in the first expression, we have 3x-12..take the 3 out in the numerator, so we have 3X(x-4) in the numerator...similarly in the denominator, take2x-8 and remove 2 ,which is common in it.so now you have 2X(x-4), .notice you have x-4 common on top and at the bottom, so they cancel each other!
ive worked out the whole problem in steps you should follow pretty easily :)
(3x-12)(x-6)(4)(x+5)(x)(x+1)
______________________
(x)(2x-8)(x^2)(2)(x+5)

as i mentioned above,remove the comon stuff and cancel x-4
similarly, we can cancel x+5 as well as the single x terms too.next simplify the numeric quantities.
so finally we're left with:
3(x+6)(x+1)
___________
2(x^2)

which works out to 3(x^2 + 7x + 6)
____________
2(x^2)


there you go!
its as simple as that :)

Answer 2

3(x-4) / x+5 * x+6 / 2(x-4)

The two x-4 cancel out
3(x+6)/ 2(x+5)

4(x+5) / x^2 * x^2 +x / 2(x+5)

the two x^2 and x+5 cancel out
4 becomes a 2 and 2 becomes a 1

2+x

Answer 3

you treat each term in the expression as variables in algebra and multiply acordingly. eg.
the first one is 3x-12/x X x+6/2x -8
This can be expressed as (a-b)*(c-d) where a is 3x, b is 12/x, c is 6/2x and d is 8

So the answer will be
(a*c) -(a*d) -(b*c)+(b*d)
Then when you replace the expressions you can cut out the common numerator and denominator and reach the result. Similarily for the second one.