SOLUTION: how to simplify x+ 3 + 2/x / 1- 4/x^2

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Question 761739: how to simplify x+ 3 + 2/x / 1- 4/x^2
Answer by khv_maths(12) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • Graphical form: x%2B3%2B%282%2Fx%29%2F%28%281-4%29%2F%28x%5E2%29%29 simplifies to x%2F3%2B3
  • Text form: x+3+(2/x)/((1-4)/(x^2)) simplifies to x/3+3
  • Cartoon (animation) form: simplify_cartoon%28+x%2B3%2B%282%2Fx%29%2F%28%281-4%29%2F%28x%5E2%29%29+%29
    For tutors: simplify_cartoon( x+3+(2/x)/((1-4)/(x^2)) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Remove unneeded parentheses around factor highlight_red%28+1%2Fx%5E2+%29
It becomes x%2B3%2B%282%2Fx%29%2F%28%281-4%29%2Fhighlight_green%28+x%5E2+%29%29.
Look at x%2B3%2Bhighlight_red%28+%28highlight_red%28+2%2Fx+%29%29%2F%28%281-4%29%2Fx%5E2%29+%29.
Remove unneeded parentheses around factor highlight_red%28+2+%29,highlight_red%28+1%2Fx+%29
It becomes x%2B3%2Bhighlight_green%28+2+%29%2Fhighlight_green%28+x+%29%2F%28%281-4%29%2Fx%5E2%29.
Look at x%2B3%2Bhighlight_red%28+2%2Fx%2F%28highlight_red%28+%281-4%29%2Fx%5E2+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2F%281-4%29+%29,highlight_red%28+x%5E2+%29
It becomes x%2B3%2B2%2Fx%2Fhighlight_green%28+%281-4%29+%29%2Ahighlight_green%28+x%5E2+%29.
Look at x%2B3%2B2%2Fx%2F%28highlight_red%28+1+%29-highlight_red%28+4+%29%29%2Ax%5E2.
Added fractions or integers together
It becomes x%2B3%2B2%2Fx%2F%28highlight_green%28+-3+%29%29%2Ax%5E2.
Look at x%2B3%2B2%2Fhighlight_red%28+x+%29%2F%28-3%29%2Ahighlight_red%28+x%5E2+%29.
Reduce similar several occurrences of highlight_red%28+1%2Fx+%29 to highlight_green%28+x%5E%28-1%2B2%29+%29
It becomes x%2B3%2B2%2Ahighlight_green%28+x%5E%28-1%2B2%29+%29%2F%28-3%29.
Look at x%2Bhighlight_red%28+3+%29%2B2%2Ax%5E%28-1%2B2%29%2F%28-3%29.
Moved 3 to the right of expression
It becomes x%2B2%2Ax%5E%28-1%2B2%29%2F%28-3%29%2Bhighlight_green%28+3+%29.
Look at x%2B2%2Ax%5E%28highlight_red%28+-1+%29%2B2%29%2F%28-3%29%2B3.
Removed extra sign in front of -1
It becomes x%2B2%2Ax%5E%28-highlight_green%28+1+%29%2B2%29%2F%28-3%29%2B3.
Look at x%2B2%2Ax%5E%28-1%2B2%29%2F%28highlight_red%28+-3+%29%29%2B3.
Removed extra sign in front of -3
It becomes x%2B2%2Ax%5E%28-1%2B2%29%2F%28-highlight_green%28+3+%29%29%2B3.
Look at x%2Bhighlight_red%28+2%2Ax%5E%28-1%2B2%29%2F%28-highlight_red%28+3+%29%29+%29%2B3.
Remove unneeded parentheses around factor highlight_red%28+1%2F3+%29
It becomes x-2%2Ax%5E%28-1%2B2%29%2Fhighlight_green%28+3+%29%2B3.
Look at x-2%2Ax%5E%28-highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2F3%2B3.
Added fractions or integers together
It becomes x-2%2Ax%5E%28highlight_green%28+1+%29%29%2F3%2B3.
Look at x-2%2Ax%5Ehighlight_red%28+%281%29+%29%2F3%2B3.
Removing power of one highlight_red%28+%281%29+%29
Look at highlight_red%28+x+%29-highlight_red%28+2%2Ax%2F3+%29%2B3.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+-2%2Ax%2F3+%29 replacing them with highlight_green%28+%281-2%2A1%2F3%29%2Ax+%29
It becomes highlight_green%28+%281-2%2A1%2F3%29%2Ax+%29%2B3.
Look at %281-highlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2F3%29%2Ax%2B3.
Multiplied numerator integers
It becomes %281-highlight_green%28+2+%29%2F3%29%2Ax%2B3.
Look at %28highlight_red%28+1+%29-highlight_red%28+2%2F3+%29%29%2Ax%2B3.
Added fractions or integers together
It becomes %28highlight_green%28+1%2F3+%29%29%2Ax%2B3.
Look at highlight_red%28+%28highlight_red%28+1%2F3+%29%29%2Ax+%29%2B3.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F3+%29
It becomes highlight_green%28+1+%29%2Fhighlight_green%28+3+%29%2Ax%2B3.
Look at highlight_red%28+1+%29%2F3%2Ax%2B3.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes x%2F3%2B3.
Result: x%2F3%2B3

Universal Simplifier and Solver


Done!