SOLUTION: 7/x-1 + 2/x+1 = 3x/x^2-1

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Question 437153: 7/x-1 + 2/x+1 = 3x/x^2-1
Answer by oberobic(2304) 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: 7%2Fx-1%2B2%2Fx%2B1=3x%2Fx%5E2-1 simplifies to 6%2Fx%2B1=0
  • Text form: 7/x-1+2/x+1=3x/x^2-1 simplifies to 6/x+1=0
  • Cartoon (animation) form: simplify_cartoon%28+7%2Fx-1%2B2%2Fx%2B1=3x%2Fx%5E2-1+%29
    For tutors: simplify_cartoon( 7/x-1+2/x+1=3x/x^2-1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 7%2Fx-highlight_red%28+1+%29%2B2%2Fx%2Bhighlight_red%28+1+%29=3x%2Fx%5E2-1.
Added fractions or integers together
It becomes 7%2Fx%2Bhighlight_green%28+0+%29%2B2%2Fx=3x%2Fx%5E2-1.
Look at 7%2Fx%2Bhighlight_red%28+0+%29%2B2%2Fx=3x%2Fx%5E2-1.
Moved 0 to the right of expression
It becomes 7%2Fx%2B2%2Fx%2Bhighlight_green%28+0+%29=3x%2Fx%5E2-1.
Look at 7%2Fx%2B2%2Fx%2Bhighlight_red%28+0+%29=3x%2Fx%5E2-1.
Remove extraneous zero highlight_red%28+0+%29
It becomes 7%2Fx%2B2%2Fx=3x%2Fx%5E2-1.
Look at highlight_red%28+7%2Fx+%29%2Bhighlight_red%28+2%2Fx+%29=3x%2Fx%5E2-1.
Eliminated similar terms highlight_red%28+7%2Fx+%29,highlight_red%28+2%2Fx+%29 replacing them with highlight_green%28+%287%2B2%29%2Fx+%29
It becomes highlight_green%28+%287%2B2%29%2Fx+%29=3x%2Fx%5E2-1.
Look at %28highlight_red%28+7+%29%2Bhighlight_red%28+2+%29%29%2Fx=3x%2Fx%5E2-1.
Added fractions or integers together
It becomes %28highlight_green%28+9+%29%29%2Fx=3x%2Fx%5E2-1.
Look at highlight_red%28+%28highlight_red%28+9+%29%29%2Fx+%29=3x%2Fx%5E2-1.
Remove unneeded parentheses around factor highlight_red%28+9+%29
It becomes highlight_green%28+9+%29%2Fx=3x%2Fx%5E2-1.
Look at 9%2Fx=3%2Ahighlight_red%28+x+%29%2Fhighlight_red%28+x%5E2+%29-1.
Reduce similar several occurrences of highlight_red%28+x+%29 to highlight_green%28+x%5E%281-2%29+%29
It becomes 9%2Fx=3%2Ahighlight_green%28+x%5E%281-2%29+%29-1.
Look at 9%2Fx=3%2Ax%5E%28highlight_red%28+1+%29-highlight_red%28+2+%29%29-1.
Added fractions or integers together
It becomes 9%2Fx=3%2Ax%5E%28highlight_green%28+-1+%29%29-1.
Look at 9%2Fx=3%2Ax%5E%28highlight_red%28+-1+%29%29-1.
Removed extra sign in front of -1
It becomes 9%2Fx=3%2Ax%5E%28-highlight_green%28+1+%29%29-1.
Look at 9%2Fx=3%2Ahighlight_red%28+x%5E%28-1%29+%29-1.
Negative power changes multiplication to division
It becomes 9%2Fx=3%2Fhighlight_green%28+x%5E1+%29-1.
Look at 9%2Fx=3%2Fx%5Ehighlight_red%28+1+%29-1.
Removing power of one highlight_red%28+1+%29
Look at 9%2Fx=highlight_red%28+3%2Fx-1+%29.
Moved these terms to the left highlight_green%28+-3%2Fx+%29,highlight_green%28+1+%29
It becomes 9%2Fx-highlight_green%28+3%2Fx+%29%2Bhighlight_green%28+1+%29=0.
Look at highlight_red%28+9%2Fx+%29-highlight_red%28+3%2Fx+%29%2B1=0.
Eliminated similar terms highlight_red%28+9%2Fx+%29,highlight_red%28+-3%2Fx+%29 replacing them with highlight_green%28+%289-3%29%2Fx+%29
It becomes highlight_green%28+%289-3%29%2Fx+%29%2B1=0.
Look at %28highlight_red%28+9+%29-highlight_red%28+3+%29%29%2Fx%2B1=0.
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Fx%2B1=0.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Fx+%29%2B1=0.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Fx%2B1=0.
Result: 6%2Fx%2B1=0

Universal Simplifier and Solver


Done!