Give the quotient in simplest form.?

Question

3x^2-xy-2y^2 / x^3-y^3 / 15x^2+10xy/ 5x^2-5xy+5y^2

It's 3x squared - xy- 2ysquared divided by x cube- y cube then divide the quotient of 15xsquared+10xy and 5xsquared-5xy+5ysquared.

Please help

Answer 1

Favorite Answer

3x^2-xy-2y^2 / x^3-y^3

= [(3x+2y)(x-y)] / [(x-y)(x^2+xy+y^2)]

= (3x+2y) / (x^2+xy+y^2)

15x^2+10xy/ 5x^2-5xy+5y^2

= [5x(3x+2y)]/[5(x^2-xy+y^2)]

= [x(3x+2y)]/(x^2-xy+y^2)

=> [(3x+2y) / (x^2+xy+y^2)] / [x(3x+2y)]/(x^2-xy+y^2)

= (x^2-xy+y^2)/ [x(x^2+xy+y^2)]

QED

Answer 2

Joelle, the trick here is to factor the expressions as best you can, then cancell the common factors and maybe multiply out the result.

So yo can write...

3x^2 -xy -2y^2 = (3x+2y)(x-y),

x^3-y^3 = (x-y)(x^2+xy+y^2)

this pair simplifies to (3x+2y)/)(x^2+xy+y^2)

15x^2+10xy=5x(3x+2y)

5x^2-5xy+5y^2=5(x^2-xy+y^2)

you should see that this pair simplifies to

x(3x+2y) / (x^2-xy+y^2)

now when you do the next division, the term (3x+2y) also vanishes so that i get

(x^2-xy+y^2)/(x(x^2+xy+y^2))

hth

Answer 3

3x^2-xy-2y^2 / x^3-y^3 / 15x^2+10xy/ 5x^2-5xy+5y^2

let:

A = 3x^2-xy-2y^2 =(x-y)(2y+3x)

B = x^3-y^3 = (x-y)(x^2+xy+y^2)

C =15x^2+10xy =5x(3x+2y)

D = 5x^2-5xy+5y^2 =5(x^2-xy+y^2)

This is A/B/C/D = (A/B) / (C/D) =

(AD)/(BC) = (A/B)*(D/C)

A/B = (x-y)(2y+3x) / {(x-y)(x^2+xy+y^2)} = (2y+3x) / (x^2+xy+y^2)

D/C = 5(x^2-xy+y^2) / {5x(3x+2y)} =

{(x^2-xy+y^2) /{x(3x+2y)}

(A/B)*(D/C) = {(2y+3x) / (x^2+xy+y^2)}*{(x^2-xy+y^2) /{x(3x+2y)} =

(x^2-xy+y^2) / {x(x^2+xy+y^2)}

Summary:

3x^2-xy-2y^2 / x^3-y^3 / 15x^2+10xy/ 5x^2-5xy+5y^2 =

(x^2-xy+y^2) / {x(x^2+xy+y^2)}

Answer 4

{ ( 3x + 2y ) ( x - y ) } / { ( x - y ) ( x^2 + xy + y^2 ) }

- all over -

{ 5x ( 3x + 2y ) } / { 5 ( x^2 - xy + y^2 ) }

5 ( 3x + 2y ) ( x - y ) ( x^2 - xy + y^2 )

- over -

5x ( x - y ) ( x^2 + xy + y^2 ) ( 3x + 2y )

cancel 5, (3x+2y) and (x-y)

giving you:

x^2 - xy + y^2

-all over-

x^2 + xy + y^2

Answer 5

cube root 162 cube root 2 * cube root 2 cube root 648 6 cube root 3 --------------------------------------... ============== cube root 2 cube root 2 * cube root 2= cube root 8= 2 ans 3 cube root 3