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1.) Find the domain of the function:

h(y) = (y^3-8) (y+2)^-3

2.) Simplify:

m^2 = m

3.) Simplify:

7x^2/9y ÷ [4x]/[15y^2]∙[35/6xy]^-1

4.) Simplify:

7/10+11/20-9/20

5.) Simplify:

2/3-3/5+4/15

6.) Simplify:

x+3/5-2x+1/10

7.) Simplify:

1/x-1/y/y/x-x/y

1.) When h(y) = (y³ - 8)/(y+2)³ is h(y) = (y-2)(y²+2y+4)/(y+2)³.

The domain is the variable possibilities, and that is all y but -2.

2.) To simplify m² = m, divide by m { noting that m can't be 0 } and get m = 1.

3.) It is not clear what [35/6xy]^-1 would be.

If it is really [35/(6xy)]^-1, then it is 6xy/35.

As written, in math, division and multiplication are both done from left to right,

so this would be 35/6 times xy, and to the -1 would gives 6/(35xy).

Once this has been determined, in proper mathematics, it would end up being times the preceding fraction, so it would be times (4x)/(15y²), but perhaps it is in the denominator.

4.) Convert all fractions to 20ths, so multiply the 1st fraction by 2/2.

This gives 14/20 + 11/20 - 9/20 = 16/20. That reduces to 4/5.

5.) Convert all fractions to 15ths. To do this, multiply the 1st by 5/5 and the 2nd by 3/3.

This gives 10/15 - 9/15 + 4/15 =5/15 = 1/3.

6.) Taking x - 2x gives -x.

Taking 3/5 + 1/10 ... multiply 3/5 by 2/2, so we have 6/10 + 1/10 = 7/10.

This makes the answer be -x + 7/10.

7.) This looks like it should really be 1/x - (1/y)/(y/x) - x/y.

Multiplying the 2nd terms by (y/x)/(y/x) gives (y/(xy))/((xy)/(xy)).

The fraction on the bottom disappears, giving y/(xy).

Since y/y is 1, this leaves 1/x for the middle term.

Rewriting what's given gives 1/x - 1/x - x/y, and this is just -x/y.

Algebra

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