SOLUTION: {{{ 1/x + (1)/(1 + x) = (-3)/(x^2 + x) }}}

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Question 308993: +1%2Fx+%2B+%281%29%2F%281+%2B+x%29+=+%28-3%29%2F%28x%5E2+%2B+x%29+
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
GreAt job using the formula system, I am impressed.
+1%2Fx+%2B+1%2F%281+%2B+x%29+=+-3%2F%28x%5E2+%2B+x%29+
combine the two fractions on the left like regular fractions
%28x%2B1%29%2Fx%2F%28x%2B1%29+%2B+x%2Fx%2F%28x%2B1%29+=+-3%2Fx%2F%28x%2B1%29
%28x%2B1%2Bx%29%2Fx%2F%28x%2B1%29+=+-3%2Fx%2Fx%2B1
%282x%2B1%2B3%29%2Fx%2F%28x%2B1%29+=+0
%282x%2B4%29%2Fx%2F%28x%2B1%29+=+0
x=-2
CHECK
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Graphical form: Equation 1%2Fx%2B1%2F%281%2Bx%29=-3%2F%28x%5E2%2Bx%29 was fully solved.
  • Text form: 1/x+1/(1+x)=-3/(x^2+x) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+1%2Fx%2B1%2F%281%2Bx%29=-3%2F%28x%5E2%2Bx%29+%29
    For tutors: simplify_cartoon( 1/x+1/(1+x)=-3/(x^2+x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 1%2Fhighlight_red%28+x+%29%2B1%2F%281%2Bx%29=-3%2F%28x%5E2%2Bx%29.
Replaced x with -2
It becomes 1%2Fhighlight_green%28+-2+%29%2B1%2F%281%2Bx%29=-3%2F%28x%5E2%2Bx%29.
Look at 1%2F-2%2B1%2F%281%2Bhighlight_red%28+x+%29%29=-3%2F%28x%5E2%2Bx%29.
Replaced x with -2
It becomes 1%2F-2%2B1%2F%281%2Bhighlight_green%28+-2+%29%29=-3%2F%28x%5E2%2Bx%29.
Look at 1%2F-2%2B1%2F%28highlight_red%28+1+%29%2Bhighlight_red%28+-2+%29%29=-3%2F%28x%5E2%2Bx%29.
Added fractions or integers together
It becomes 1%2F-2%2B1%2F%28highlight_green%28+-1+%29%29=-3%2F%28x%5E2%2Bx%29.
Look at highlight_red%28+1%2F-2+%29%2Bhighlight_red%28+1%2F%28-1%29+%29=-3%2F%28x%5E2%2Bx%29.
Replace constants in expression: highlight_red%28+1%2F-2+%29,highlight_red%28+1%2F%28-1%29+%29 with highlight_green%28+-1.5+%29
It becomes highlight_green%28+-1.5+%29=-3%2F%28x%5E2%2Bx%29.
Look at highlight_red%28+-1.5+%29=-3%2F%28x%5E2%2Bx%29.
Removed extra sign in front of -1.5
It becomes -highlight_green%28+1.5+%29=-3%2F%28x%5E2%2Bx%29.
Look at -1.5=-3%2F%28highlight_red%28+x+%29%5E2%2Bx%29.
Replaced x with -2
It becomes -1.5=-3%2F%28highlight_green%28+-2+%29%5E2%2Bx%29.
Look at -1.5=-3%2F%28highlight_red%28+-2+%29%5Ehighlight_red%28+2+%29%2Bx%29.
Replace constants in factor: highlight_red%28+-2+%29,highlight_red%28+2+%29 with highlight_green%28+4+%29
It becomes -1.5=-3%2F%28highlight_green%28+4+%29%2Bx%29.
Look at -1.5=-3%2F%284%2Bhighlight_red%28+x+%29%29.
Replaced x with -2
It becomes -1.5=-3%2F%284%2Bhighlight_green%28+-2+%29%29.
Look at -1.5=-3%2F%28highlight_red%28+4+%29%2Bhighlight_red%28+-2+%29%29.
Added fractions or integers together
It becomes -1.5=-3%2F%28highlight_green%28+2+%29%29.
Look at -1.5=-highlight_red%28+3%2F%28highlight_red%28+2+%29%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1%2F2+%29
It becomes -1.5=-3%2Fhighlight_green%28+2+%29.
Look at -1.5=highlight_red%28+-3%2F2+%29.
Moved these terms to the left highlight_green%28+3%2F2+%29
It becomes -1.5%2Bhighlight_green%28+3%2F2+%29=0.
Look at -highlight_red%28+1.5+%29%2Bhighlight_red%28+3%2F2+%29=0.
Added fractions or integers together
It becomes highlight_green%28+0%2F10+%29=0.
Look at highlight_red%28+0+%29%2Fhighlight_red%28+10+%29=0.
Factors 0 and 10 have greatest common factor (GCF) of 10. Reducing fraction.
It becomes highlight_green%28+0+%29%2Fhighlight_green%28+1+%29=0.
Look at highlight_red%28+0%2F1+%29=0.
Since highlight_red%28+0%2F1+%29 has zero as a factor, it should be replaced with a zero
Look at 0=0.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 0=0.
Result: 0=0

Universal Simplifier and Solver


Done!