Simplifying Rational Expressions 4x-12 over 2x-6 and 21-3x over x^2 - 3x - 28?

Question

These two problems i did but messed up somewhere im not sure what I did wrong can you please take me threw step by step.
just incase it was hard to read
1) 4x-12 / 2x-6
2) 21-3x / x^2 - 3x - 28

Answer 1

1) (4x - 12) / (2x - 6)

Your first step is to factor top and bottom. Factor the greatest common factor for each one.

[ 4(x - 3) ] / [ 2(x - 3) ]

Now, note the common factor on the top and the bottom, of
(x - 3). Cancel. This leaves us with

4/2

Which we can again reduce, as just 2.

2) (21 - 3x) / (x^2 - 3x - 28)

First, factor top and bottom

[ 3(7 - x) ] / [ (x - 7)(x + 4) ]

Use the "negative one" technique to swap (7 - x) into (x - 7). This involves factoring out (-1). In other words,
b - a = (-1)(a - b), if we ever want to swap terms.

[ 3(-1)(x - 7) ] / [ (x - 7)(x + 4) ]

Cancel the common factor of (x - 7) on top and bottom.

[ 3(-1) ] / [ (x + 4) ]

Simplify.

-3/(x + 4)

Answer 2

1. 4x-12/2x-6=
4(x-3)/2(x-3)
x-3 cancels out ,and 4 is divided by 2 to give 2 .
hence, the ans is 2

2. 21-3x/x^2-3x-28=
3(7-x)/x^2-7x+4x -28=
3(7-x)/x(x-7)+4(x-7)=
3(7-x)/(x+4)(x-7) = 3(7-x)/-(7+x)(x+4)= 3/-(x+4)
that is, 7-x cancels out.
answer = 3/-(x+4) or -3/(x+4)

Answer 3

4x-12 / 2x-6 =
2(2x-6) / 2x-6=
2



21-3x / x^2 -3x-28 =
3(7-x) / (x-7)(x+4) =
-3(x-7) / (x-7)(x+4) =
-3 / x+4

Answer 4

for x^2-12x+35 discover 2 numbers which the multiply is 35 and sum is -12 so we've -7 & -5 for x^2-3x-28 ind 2 numbers which the multply is -28 and sum is -3 so we've 4 & -7 (x-7)(x-5) -------------- (x-7)(x+4) so (x-7) will cancel the shall we've (x-5) --------- (x-4)

Answer 5

1. 4(x-3)
-----------
2(x-3)

x-3 cancel out and the 4 becomes a 2 and the 2 becomes a 1 answer= 2

2.-3(x-7)
-------------
(x+4)(x-7)

x-7 cancel out

answer = -3/x+4

Answer 6

Hi
pl.contact me for solution.
I have master degree in mathematics and I have got
thirteen years of teaching experience in math at college level, and currently I am working as a lecturer for an army engineering college author of math guide.
hi
i can within 10 minutes for $2

Answer 7

1)4x-12/2x-6
4(x-3)/2(x-3)
2

2)21-3x/x^2-3x-28
-3x+21/x^2-3x-28
-3(x-7)/(x-7)(x+4)
-3/(x+4)

I hope this helps!

Answer 8

why do you want to read it ?
is it your Challenge or someting else tell me about it