SOLUTION: Do the operations and simplify. 1.(x^2+4x+4/x) * (x^2 - 2x/x^2 -4) 2.(x^2 + 2x - 63/9x^2 +71x +56) * (81x^2 - 64/ 9x^2 +73x - 72)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Do the operations and simplify. 1.(x^2+4x+4/x) * (x^2 - 2x/x^2 -4) 2.(x^2 + 2x - 63/9x^2 +71x +56) * (81x^2 - 64/ 9x^2 +73x - 72)      Log On


   



Question 111456: Do the operations and simplify.
1.(x^2+4x+4/x) * (x^2 - 2x/x^2 -4)



2.(x^2 + 2x - 63/9x^2 +71x +56) * (81x^2 - 64/ 9x^2 +73x - 72)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%5E2%2B4x%2B4%29%2Fx%29+%2A+%28%28x%5E2+-+2x%29%2F%28x%5E2+-4%29%29%29........ I guess your equation should be writen this way

%28%28x%5E2%2B4x%2B4%29%2Fx%29+%2A+%28%28x%5E2+-+2x%29%2F%28x%5E2+-4%29%29%29........ in first term, write
4x as 2x+%2B+2x then group first two and second two terms

........factor out
........reduce x%2B2 and x%2B2, then x-2 and x-2 in nominator and denominator

%28%28x%2B2%29%2Fx%29+%2A+x%29........reduce x and x
finaly, you will have:
x%2B2........

2.......
first we can do some factorization:
look first this expression:
x%5E2+%2B+2x+-+63
Replace 2x with -7x+%2B+9x and group the first two terms together
and the last two terms together like this:
%28x%5E2+-+7x%29+%2B+%289x+-+63%29……

factor a 1x out of the first group and factor a 9 out of the
second group
1x%28x+-+7%29+%2B+9%28x+-+7%29…… factor a x+%96+7 out
and you will have:
%28x+%2B+9%29%28x-7%29

then, look at this expression: 9x%5E2+%2B71x+%2B56
Replace 71x with 8x+%2B+63x and group the first two terms together
and the last two terms together like this:
%289x%5E2+%2B+8x%29+%2B+%2863x+%2B+56%29……
factor a 1x out of the first group and factor a 7 out of the second group
1x%289x+%2B+8%29+%2B+7%289x+%2B+8%29…… factor a %289x+%2B+8%29 out
and you will have:
%289x+%2B+8%29%28x%2B7%29


then, this expression 81x%5E2+-+64we can write as %289x%29%5E2+-+8%5E2+=+%289x+-+8%29%289x+%2B+8%29

at the end, take a look at this expression:
9x%5E2+%2B73x+-+72
Replace 73x with -8x+%2B+81x and group the first two terms together
and the last two terms together like this:
%289x%5E2+-+8x%29+%2B+%2881x+-+72%29……
factor a 1x out of the first group and factor a 9 out of the second group
1x%289x+-+8%29+%2B+9%289x+-+8%29…… factor a %289x+-+8%29 out
and you will have:
%289x+-+8%29%28x%2B+9%29

now, substitute all of this in :


...reduce

%28x-7%29%2F%28x%2B7%29...