Simplify math problems could some one please help>?

Question

Could someone please help me with these math problems please.. thanks..

1. Simplify completely 9x+18 / x+ 2
A) 9(x+2) / (x+2)
B) 15
C) 9
D) 9x +6 / x

2. simplify completely x^2 -25 / x^2 +3x -10
A) (x+5)(x-5) / (x+5)(x-2)
B) x+5 / x+2
C) -25 / 3x -10
D) x - 5 / x-2

3. simplify completely (3x - 6) / (x^2 - 9) * (x+3) / (x^2 -2x)
A) 3 / x(x-3)
B) 3 / x(x+3)
C) 3 / x
D) 3 / x-3

4. simplify completely (x^2 +4x+4) / 20 divide (x+2) / 10
A) x+ 2
B) x-2 /2
C) x+2 / 2
D) 2(x+2)

Answer 1

1. C
2. D
3. A
4. C

The first two, answer A is the factoring and then you can see the cancelling to do. The third one just looks wretched but is easy once you have a single fraction and cancel. The fourth one is straightforward as well, hard to see how the first answerer got it wrong.

Of course, you really need a few more parentheses to properly state the answers!

Finally, if you had equations rather than just binomials, you would have to pay attention to the factors before you cancel since some answers an equation might generate could be forbidden by the fact they would make the interim step/s divide by zero. For instance, in the first one, if you had an equation that yielded x = –2 after all the factoring, cancelling and algebraic shuffling was done, then there would be no answer because x + 2 (which you divide by in the original statement of the problem) would be 0. Not that it matters here, but when you begin using the factoring and cancelling techniques with equations it is something to always keep in mind.

Answer 2

1. 9x+18 / x+2
9(x+2)/ (x+2)=the (x+2 )cancel out
Answer 9

2. x^2-25/x^2=3X-10
(x-5)(x+5)/(x-2)(x+5)
the 2 X+5 cancel out
Answer (x-5)/ (x-2)

3. 3x-6/x^2-9 * (x+3) / x^2-2x
3(x-2)/(x-3)(x+3) *(x+3/ x(x-2)
the x+3 and x-2 cancel out
Answer 3/ x(x-3)

4. (x^2 +4x+4 / 20 divide (x+2) / 10
(x+2)(x+2)/20 * 10/(x+2)=

2 of the 3 (x+2) cancel out and the 10 becomes 1 and 20 becomes 2
Answer x+2 /2

Answer 3

1) Simply completely:

9x+18/x+2
9(x+2)/x+2
9* (x+2)/(x+2)
9*1
9

Answer: C

2) x^2-25/x^2+3x-10

x^2-25 factors out to (x+5)(x-5)
x^2+3x-10 factors out to (x-2)(x+5)

so:

(x+5)(x-5)/(x-2)(x+5)
(x-5)/(x-2)

Answer: D

3) (3x-6)/(x^2-9) * (x+3)/(x^2-2x)

x^2-9 factors to (x+3)(x-3)
x^2-2x factors to (x-2)(x[+0])

so:

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

Answer: A

4) ((x^2 +4x+4)/20)/((x+2)/10)

x^2+4x+4 factors to a perfect square, so (x+2)(x+2)

Dividing fractions (same concept here ), you flip and multiply.

so:

(x+2)(x+2)/20 * 10/(x+2)
10(x+2)(x+2)/20(x+2)
(x+2)/2

Answer: C

Answer 4

1. C

2. D

3. A

4. B