document.write( "Question 388150: Multiply and simplify:\r
\n" ); document.write( "\n" ); document.write( "(x^2 - 4x + 3/4x + 4) * (x + 1/x^2 + 2x - 3)
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Algebra.Com's Answer #274516 by Jk22(389)\"\" \"About 
You can put this solution on YOUR website!
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Solved by pluggable solver: Add, Subtract and Multiply Polynomials and Simplify
Your Result:

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  • Graphical form: \"%28x%5E2-4x%2B3%2F4%2Ax%2B4%29%2A%28x%2B1%2Fx%5E2%2B2%2Ax-3%29\" simplifies to \"x%5E%283%29%2A3-51%2F4%2Ax%5E2-13%2F4%2Fx%2B87%2F4%2Ax%2B4%2Fx%5E2-11\"
  • Text form: (x^2-4x+3/4*x+4)*(x+1/x^2+2*x-3) simplifies to x^(3)*3-51/4*x^2-13/4/x+87/4*x+4/x^2-11
  • Cartoon (animation) form: \"simplify_cartoon%28+%28x%5E2-4x%2B3%2F4%2Ax%2B4%29%2A%28x%2B1%2Fx%5E2%2B2%2Ax-3%29+%29\"
    For tutors: simplify_cartoon( (x^2-4x+3/4*x+4)*(x+1/x^2+2*x-3) )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at .
Eliminated similar terms \"highlight_red%28+-4%2Ax+%29\",\"highlight_red%28+3%2F4%2Ax+%29\" replacing them with \"highlight_green%28+%28-4%2B3%2A1%2F4%29%2Ax+%29\"
It becomes .
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Look at .
Eliminated similar terms \"highlight_red%28+x+%29\",\"highlight_red%28+2%2Ax+%29\" replacing them with \"highlight_green%28+%281%2B2%29%2Ax+%29\"
It becomes .
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Look at .
Multiplied numerator integers
It becomes .
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Look at .
Added fractions or integers together
It becomes .
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Look at .
Added fractions or integers together
It becomes \"%28x%5E2%2B%28-13%2F4%29%2Ax%2B4%29%2A%28%28highlight_green%28+3+%29%29%2Ax%2B1%2Fx%5E2-3%29\".
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Look at .
Remove unneeded parentheses around factor \"highlight_red%28+13+%29\",\"highlight_red%28+1%2F4+%29\"
It becomes .
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Look at .
Remove unneeded parentheses around factor \"highlight_red%28+3+%29\"
It becomes \"%28x%5E2-13%2F4%2Ax%2B4%29%2A%28highlight_green%28+3+%29%2Ax%2B1%2Fx%5E2-3%29\".
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Look at \"highlight_red%28+%28x%5E2-13%2F4%2Ax%2B4%29%2A%283%2Ax%2B1%2Fx%5E2-3%29+%29\".
Expanded term \"%283%2Ax%2B1%2Fx%5E2-3%29\" by using associative property on \"%28x%5E2-13%2F4%2Ax%2B4%29\"
It becomes .
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Look at .
Expanded term \"x%5E2\" by using associative property on \"%283%2Ax%2B1%2Fx%5E2-3%29\"
It becomes .
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Look at .
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes .
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Look at .
Reduce similar several occurrences of \"highlight_red%28+x%5E2+%29\" to \"highlight_green%28+x%5E%281%2B2%29+%29\"
It becomes .
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Look at .
Reduce similar several occurrences of \"highlight_red%28+x%5E2+%29\" to \"highlight_green%28+x%5E%282-2%29+%29\"
It becomes .
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Look at .
Added fractions or integers together
It becomes .
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Look at .
Added fractions or integers together
It becomes .
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Look at .
Removing power \"highlight_red%28+x+%29\" to degree of \"highlight_green%28+%280%29+%29\"
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Look at .
Moved \"1\" to the right of expression
It becomes .
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Look at .
Expanded term \"-13%2F4%2Ax\" by using associative property on \"%283%2Ax%2B1%2Fx%5E2-3%29\"
It becomes .
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Look at .
Multiplied numerator integers
It becomes .
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Look at .
Multiplied numerator integers
It becomes .
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Look at .
Multiplied numerator integers
It becomes .
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Look at .
Reduce similar several occurrences of \"highlight_red%28+x+%29\" to \"highlight_green%28+x%5E2+%29\"
It becomes .
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Look at .
Reduce similar several occurrences of \"highlight_red%28+x+%29\" to \"highlight_green%28+x%5E%281-2%29+%29\"
It becomes .
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Look at .
Added fractions or integers together
It becomes .
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Look at .
Removed extra sign in front of \"-1\"
It becomes .
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Look at .
Eliminated similar terms \"highlight_red%28+-x%5E2%2A3+%29\",\"highlight_red%28+-39%2F4%2Ax%5E2+%29\" replacing them with \"highlight_green%28+%28-3-39%2A1%2F4%29%2Ax%5E2+%29\"
It becomes .
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Look at .
Multiplied numerator integers
It becomes .
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Look at .
Added fractions or integers together
It becomes .
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Look at .
Remove unneeded parentheses around factor \"highlight_red%28+51+%29\",\"highlight_red%28+1%2F4+%29\"
It becomes .
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Look at .
Negative power changes multiplication to division
It becomes .
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Look at .
Removing power of one \"highlight_red%28+1+%29\"
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Look at .
Expanded term \"4\" by using associative property on \"%283%2Ax%2B1%2Fx%5E2-3%29\"
It becomes .
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Look at .
Multiplied numerator integers
It becomes .
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Look at .
Multiplied numerator integers
It becomes .
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Look at .
Multiplied numerator integers
It becomes .
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Look at .
Added fractions or integers together
It becomes .
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Look at .
Removed extra sign in front of \"-11\"
It becomes .
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Look at .
Eliminated similar terms \"highlight_red%28+39%2F4%2Ax+%29\",\"highlight_red%28+12%2Ax+%29\" replacing them with \"highlight_green%28+%2839%2A1%2F4%2B12%29%2Ax+%29\"
It becomes .
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Look at .
Multiplied numerator integers
It becomes .
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Look at .
Added fractions or integers together
It becomes .
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Look at .
Remove unneeded parentheses around factor \"highlight_red%28+87+%29\",\"highlight_red%28+1%2F4+%29\"
It becomes .
Result: \"x%5E%283%29%2A3-51%2F4%2Ax%5E2-13%2F4%2Fx%2B87%2F4%2Ax%2B4%2Fx%5E2-11\"
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Universal Simplifier and Solver

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Done!
x^(3)*3-51/4*x^2-13/4/x+87/4*x+4/x^2-11
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