SOLUTION: (6/2x-2)-(1/x+1)=(2/2x+2)+1

Algebra ->  Equations -> SOLUTION: (6/2x-2)-(1/x+1)=(2/2x+2)+1      Log On


   

Question 213791This question is from textbook College Algebra
: (6/2x-2)-(1/x+1)=(2/2x+2)+1 This question is from textbook College Algebra

Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
use y=1/x and get:
%286%2F2x-2%29-%281%2Fx%2B1%29=%282%2F2x%2B2%29%2B1 or %286%2F2%2Ay-2%29-%28y%2B1%29=%282%2F2%2Ay%2B2%29%2B1
solve this now
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: y=6.
  • Graphical form: Equation %286%2F2%2Ay-2%29-%28y%2B1%29=%282%2F2%2Ay%2B2%29%2B1 was fully solved.
  • Text form: (6/2*y-2)-(y+1)=(2/2*y+2)+1 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+%286%2F2%2Ay-2%29-%28y%2B1%29=%282%2F2%2Ay%2B2%29%2B1+%29
    For tutors: simplify_cartoon( (6/2*y-2)-(y+1)=(2/2*y+2)+1 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+%286%2F2%2Ay-2%29+%29-%28y%2B1%29=%282%2F2%2Ay%2B2%29%2B1.
Remove unneeded parentheses around terms highlight_red%28+6%2F2%2Ay+%29,highlight_red%28+-2+%29
It becomes .
Look at 6%2F2%2Ay-2-highlight_red%28+%28y%2B1%29+%29=%282%2F2%2Ay%2B2%29%2B1.
Remove unneeded parentheses around terms highlight_red%28+-y+%29,highlight_red%28+-1+%29
It becomes 6%2F2%2Ay-2-highlight_green%28+y+%29-highlight_green%28+1+%29=%282%2F2%2Ay%2B2%29%2B1.
Look at highlight_red%28+6+%29%2Fhighlight_red%28+2+%29%2Ay-2-y-1=%282%2F2%2Ay%2B2%29%2B1.
Factors 6 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes highlight_green%28+3+%29%2Fhighlight_green%28+1+%29%2Ay-2-y-1=%282%2F2%2Ay%2B2%29%2B1.
Look at 3%2F1%2Ay-highlight_red%28+2+%29-y-highlight_red%28+1+%29=%282%2F2%2Ay%2B2%29%2B1.
Added fractions or integers together
It becomes 3%2F1%2Ay%2Bhighlight_green%28+-3+%29-y=%282%2F2%2Ay%2B2%29%2B1.
Look at 3%2F1%2Ay%2Bhighlight_red%28+-3+%29-y=%282%2F2%2Ay%2B2%29%2B1.
Moved -3 to the right of expression
It becomes 3%2F1%2Ay-y%2Bhighlight_green%28+-3+%29=%282%2F2%2Ay%2B2%29%2B1.
Look at 3%2F1%2Ay-y%2Bhighlight_red%28+-3+%29=%282%2F2%2Ay%2B2%29%2B1.
Removed extra sign in front of -3
It becomes 3%2F1%2Ay-y-highlight_green%28+3+%29=%282%2F2%2Ay%2B2%29%2B1.
Look at 3%2Fhighlight_red%28+1+%29%2Ay-y-3=%282%2F2%2Ay%2B2%29%2B1.
Remove extraneous '1' from product highlight_red%28+1%2F1+%29
It becomes 3%2Ay-y-3=%282%2F2%2Ay%2B2%29%2B1.
Look at highlight_red%28+3%2Ay+%29-highlight_red%28+y+%29-3=%282%2F2%2Ay%2B2%29%2B1.
Eliminated similar terms highlight_red%28+3%2Ay+%29,highlight_red%28+-y+%29 replacing them with highlight_green%28+%283-1%29%2Ay+%29
It becomes highlight_green%28+%283-1%29%2Ay+%29-3=%282%2F2%2Ay%2B2%29%2B1.
Look at %28highlight_red%28+3+%29-highlight_red%28+1+%29%29%2Ay-3=%282%2F2%2Ay%2B2%29%2B1.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2Ay-3=%282%2F2%2Ay%2B2%29%2B1.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2Ay+%29-3=%282%2F2%2Ay%2B2%29%2B1.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2Ay-3=%282%2F2%2Ay%2B2%29%2B1.
Look at 2%2Ay-3=highlight_red%28+%282%2F2%2Ay%2B2%29+%29%2B1.
Remove unneeded parentheses around terms highlight_red%28+2%2F2%2Ay+%29,highlight_red%28+2+%29
It becomes 2%2Ay-3=highlight_green%28+2%2F2%2Ay+%29%2Bhighlight_green%28+2+%29%2B1.
Look at 2%2Ay-3=highlight_red%28+2+%29%2Fhighlight_red%28+2+%29%2Ay%2B2%2B1.
Factors 2 and 2 have greatest common factor (GCF) of 2. Reducing fraction.
It becomes 2%2Ay-3=highlight_green%28+1+%29%2Fhighlight_green%28+1+%29%2Ay%2B2%2B1.
Look at 2%2Ay-3=1%2F1%2Ay%2Bhighlight_red%28+2+%29%2Bhighlight_red%28+1+%29.
Added fractions or integers together
It becomes 2%2Ay-3=1%2F1%2Ay%2Bhighlight_green%28+3+%29.
Look at 2%2Ay-3=highlight_red%28+1+%29%2Fhighlight_red%28+1+%29%2Ay%2B3.
Reduce similar several occurrences of highlight_red%28+1+%29 to
It becomes 2%2Ay-3=y%2B3.
Look at 2%2Ay-3=highlight_red%28+y%2B3+%29.
Moved these terms to the left highlight_green%28+-y+%29,highlight_green%28+-3+%29
It becomes 2%2Ay-3-highlight_green%28+y+%29-highlight_green%28+3+%29=0.
Look at 2%2Ay-highlight_red%28+3+%29-y-highlight_red%28+3+%29=0.
Added fractions or integers together
It becomes 2%2Ay%2Bhighlight_green%28+-6+%29-y=0.
Look at 2%2Ay%2Bhighlight_red%28+-6+%29-y=0.
Moved -6 to the right of expression
It becomes 2%2Ay-y%2Bhighlight_green%28+-6+%29=0.
Look at 2%2Ay-y%2Bhighlight_red%28+-6+%29=0.
Removed extra sign in front of -6
It becomes 2%2Ay-y-highlight_green%28+6+%29=0.
Look at highlight_red%28+2%2Ay+%29-highlight_red%28+y+%29-6=0.
Eliminated similar terms highlight_red%28+2%2Ay+%29,highlight_red%28+-y+%29 replacing them with highlight_green%28+%282-1%29%2Ay+%29
It becomes highlight_green%28+%282-1%29%2Ay+%29-6=0.
Look at highlight_red%28+%282-1%29+%29%2Ay-6=0.
Remove extraneous '1' from product highlight_red%28+%282-1%29+%29
It becomes y-6=0.
Look at highlight_red%28+y-6+%29=0.
Solved linear equation highlight_red%28+y-6=0+%29 equivalent to y-6 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=6.

Universal Simplifier and Solver


Done!


since y = 6, then x+=+1%2Fy+=+1%2F6