Simplify... and please explain your answer.?

Question

16x^2y / 48xy^3

5xy-3y / 9-15x

x^2 + 5x + 6 / x^2 + 8x + 15

3x^2 - 12x / 6x^3 - 24x^2 + 24x

Thanks you so much for anyone who takes the time to help. I am having a hard time learning this stuff on my own. Thanks again.

Answer 1

16x^2y / 48xy^3 = (16/48)(x^2/x)(y/y^3) = (1/3)(x/1)(1/y^2) = 3x/y^2

(5xy-3y) / (9-15x)
y(5x - 3)/[3(3 - 5x)]
Note that 3 - 5x = -(5x - 3)
-y(5x - 3)/[3(5x - 3)]
-y/3

(x^2 + 5x + 6) / (x^2 + 8x + 15)
(x + 2)(x + 3)/[(x + 3)(x + 5)]
(x + 2)/(x + 5)

(3x^2 - 12x) / (6x^3 - 24x^2 + 24x)
[3x(x - 4)]/[6x(x^2 - 4x + 4)]
[3x(x - 4)]/[6x(x - 2)(x - 2)]
(x - 4)/[2(x - 2)^2]
Are you sure you wrote this one right? I would expect more to cancel

Answer 2

In the first one you reduce your coefficients and then apply your laws of exponents to reduce the powers. When dividing powers with the same base you subtract exponents; when multiplying, you add exponents.
16x^2 / 48xy^3 = 1^x / 3y^2
In the other three you must look for a common factor, this can be a variable or a coefficient. Once you take out this factor you may be able to further factor the expression. You could also be left with identical expressions in the numerator and denominator. These can 'cancel each other out', however you must put restrictions such as x can't equal 1. These restrictions are defined by what value of x makes the denominator equal 0 (which makes the expression undefined).

2) y(5x-3) / 3(3-5x) = y(5x-3) / -3(5x-3) = - y / 3
x can't be 5/3
If you have the same terms within the bracket but they are in the wrong order, you factor out -1 to switch the order.
3) (x+2)(x+3) / (x+3)(x+5) = (x+2) / (x+5)
x can't be -3, -5
4) 3x(x-4) / 6x(x^2 - 4x + 4) = (x-4) / 2(x-2)^2

Answer 3

16x^2y / 48xy^3

x/3y^2 *get its GCF and divid numerator and denominator for this,the GCF is 16xy

so
16x^2y/16xy = 1xy^0 *you can just remove 1 and y^o because y^0 is negative 1. so the simplified numerator is x

for the denominator
48xy^3/16xy = 3y^2 *use same method above

5xy-3y / 9-15xy *simplify -15x+9 so it will become -3(5x - 3) also simplify 5xy - 3y by putting the y outside it will become y(5x - 3)

y(5x -3)/ -3(5x - 3) *cancel 5x - 3

the answer is

y/-3 or -(y/3)

x^2 + 5x + 6 / x^2 + 8x + 15 *factor out

x^2 + 5x + 6 = (x + 3)(x + 2)
x^2 + 8x + 15 = (x +3)(x+5)
*cancel x+3 it will become
x+2/x+5

3x^2 - 12x / 6x^3 - 24x^2 + 24x
*is also equal to
3x(x - 4)/3x(2x^2 - 8x +8) *cancel 3x then get factors of denominator

(2x - 4)(x -2) then simplify 2x - 4 = 2(x -2)(x-2)

the answer is

x-4 / 2(x-2)(x-2)

Answer 4

16x^2y / 48xy^3 = x / 3y^2
You divide 16/48 simple enough.
You divide x^2 by x
You divide y by y^3, which leaves y^2 in the denominator

(5xy-3y) / (9-15x) =
y(5x-3) / (-3)(5x -3) factoring =
y/(-3) = -y/3

(x^2 + 5x + 6) / (x^2 + 8x + 15) factor top and bottom =
(x + 2) (x + 3) / (x+3) (x+5) divide top and bottom by (x+3)
(x +2) / (x+5)

(3x^2 - 12x) / (6x^3 - 24x^2 + 24x) divide everything by 3x
(x - 4) / (2x^2 - 8x + 8) factor
(x - 4) / 2(x -2)(x-2)

Answer 5

16x^2y / 48xy^3 = x/3y^2

(5xy-3y( / (9-15x) = y(5x-3)/-3(5x-3) = -y/3

(x^2 + 5x + 6) /( x^2 + 8x + 15)
= (x+2)(x+3)/[(x+5)(x+3)] = (x+2)/(x+5)

(3x^2 - 12x) / (6x^3 - 24x^2 + 24x)
= 3x(x-4)/[6x(x-2)^2] = (x-4)/[3(x-2)^2]