how to reduce the given expressions into its simplest form?

Question

1. x^2y / xy
2. 3(x-2)^2 / 6(x-2)^4
3. x^3y(2x-1) / x+y^2 (2x+1)
4. 15x-5 / 5x+25
could you pls. tell me how did you solve to get the answer.

Answer 1

1.) (x^2y)/(xy) = ((x)(x)(y))/(x)(y) = (x/x)(y/y)(x) = (1)(1)(x) = x

2.) (3(x-2)^2)/(6(x-2)^4) = ((3)(x-2)(x-2))/((3)(2)(x-2)(x-2)(x-2)^2)
*Now what can be "1"

3.) There may be a type-o in the denom having the "+" sign, but if such the case, the expression is at it's simplest form.

4.) Now for this think about factoring out a number and I think you'll see something that can be in its simplest form.

Answer 2

1. x^y / xy = xxy / xy = x
Cancel out x and y
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2. 3(x-2)^2 / 6(x-2)^4 = (x-2)^2 / 2(x-2)^4 = 1 / 2(x-2)^2 = 1 / 2(x^2 - 4x +4) = 2x^2 -8x +8
Cancel out the common factors i.e. 3 and (x-2)
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3. x^3y(2x-1) / x+y^2 (2x+1)
There is no common factor, hence it cannot be simplified any further.
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4. 15x-5 / 5x+25 = 5(3x-1) / 5(x+5) = 3x-1 / x+5
Remove the common factor i.e. 5 from the brackets and cancel it out from the numerator and the denominator

Answer 3

1) x^2y/ x = x^(2y-1) and so 1)x^2y /xy = x (2y-1) y^-1

2) (x-2)^2/ (x-2)^4 = (x-2)^-2 and 3/6 = 1/2 so 2 ) 0.5/ (x-2)2

3) multiply numerator and denominator by (2x+1) . here i have no more ideas

4 ) divide numerator and denominator by 5

3x-1/ x+5

Answer 4

1. factor out each term if necessary
2. cancel similar factors between the numerator and denominator.
3. factors not cancelled out consist the simplified form

example:

x^2y / xy
given expression


(x)(x)(y)
________
xy
here you can cancel 'x' & 'y' between the numerator & denominator


x

is the simplest form



good luck with the rest!!!!

Answer 5

1. x
2. 1/2(x-2)^2
3. dunno
4. 3x-1/x+5

Answer 6

1. x
2. 1/(x-2)^2
3. & 4. are not possible. [e-mail]