Algebra Solver and Math Simplifier that SHOWS WORK

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Expression Simplifier and Solver
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  • Graphical form: %281%2F4%29%2A%284%2Ax-4%29=%281%2F5%29%2A%285%2Ax-10%29 simplifies to 1=0
  • Text form: (1/4)*(4*x-4)=(1/5)*(5*x-10) simplifies to 1=0
  • Cartoon (animation) form: simplify_cartoon%28+%281%2F4%29%2A%284%2Ax-4%29=%281%2F5%29%2A%285%2Ax-10%29+%29
    For tutors: simplify_cartoon( (1/4)*(4*x-4)=(1/5)*(5*x-10) )
  • 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+%29,highlight_red%28+1%2F4+%29
It becomes .
Look at highlight_red%28+1+%29%2F4%2A%284%2Ax-4%29=%281%2F5%29%2A%285%2Ax-10%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %284%2Ax-4%29%2F4=%281%2F5%29%2A%285%2Ax-10%29.
Look at %284%2Ax-4%29%2F4=highlight_red%28+%28highlight_red%28+1%2F5+%29%29%2A%285%2Ax-10%29+%29.
Remove unneeded parentheses around factor highlight_red%28+1+%29,highlight_red%28+1%2F5+%29
It becomes %284%2Ax-4%29%2F4=highlight_green%28+1+%29%2Fhighlight_green%28+5+%29%2A%285%2Ax-10%29.
Look at %284%2Ax-4%29%2F4=highlight_red%28+1+%29%2F5%2A%285%2Ax-10%29.
Remove extraneous '1' from product highlight_red%28+1+%29
It becomes %284%2Ax-4%29%2F4=%285%2Ax-10%29%2F5.
Look at %284%2Ax-4%29%2F4=highlight_red%28+%285%2Ax-10%29%2F5+%29.
Moved these terms to the left highlight_green%28+-%285%2Ax-10%29%2F5+%29
It becomes %284%2Ax-4%29%2F4-highlight_green%28+%285%2Ax-10%29%2F5+%29=0.
Look at highlight_red%28+%284%2Ax-4%29%2F4+%29-%285%2Ax-10%29%2F5=0.
Expanded term 1%2F4 by using associative property on %284%2Ax-4%29
It becomes highlight_green%28+1%2F4%2A4%2Ax+%29-highlight_green%28+1%2F4%2A4+%29-%285%2Ax-10%29%2F5=0.
Look at 1%2Fhighlight_red%28+4+%29%2Ahighlight_red%28+4+%29%2Ax-1%2F4%2A4-%285%2Ax-10%29%2F5=0.
Factors 4 and 4 have greatest common factor (GCF) of 4. Reducing fraction.
It becomes 1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+1+%29%2Ax-1%2F4%2A4-%285%2Ax-10%29%2F5=0.
Look at highlight_red%28+1+%29%2F1%2Ahighlight_red%28+1+%29%2Ax-1%2F4%2A4-%285%2Ax-10%29%2F5=0.
Multiplied numerator integers
It becomes highlight_green%28+1+%29%2F1%2Ax-1%2F4%2A4-%285%2Ax-10%29%2F5=0.
Look at 1%2F1%2Ax-1%2Fhighlight_red%28+4+%29%2Ahighlight_red%28+4+%29-%285%2Ax-10%29%2F5=0.
Factors 4 and 4 have greatest common factor (GCF) of 4. Reducing fraction.
It becomes 1%2F1%2Ax-1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+1+%29-%285%2Ax-10%29%2F5=0.
Look at 1%2F1%2Ax-highlight_red%28+1+%29%2F1%2Ahighlight_red%28+1+%29-%285%2Ax-10%29%2F5=0.
Multiplied numerator integers
It becomes 1%2F1%2Ax-highlight_green%28+1+%29%2F1-%285%2Ax-10%29%2F5=0.
Look at highlight_red%28+1+%29%2Fhighlight_red%28+1+%29%2Ax-1%2F1-%285%2Ax-10%29%2F5=0.
Reduce similar several occurrences of highlight_red%28+1+%29 to
It becomes x-1%2F1-%285%2Ax-10%29%2F5=0.
Look at x-highlight_red%28+1+%29%2Fhighlight_red%28+1+%29-%285%2Ax-10%29%2F5=0.
Reduce similar several occurrences of highlight_red%28+1+%29 to highlight_green%28+1+%29
It becomes x-highlight_green%28+1+%29-%285%2Ax-10%29%2F5=0.
Look at x-highlight_red%28+1+%29-%285%2Ax-10%29%2F5=0.
Moved -1 to the right of expression
It becomes x-%285%2Ax-10%29%2F5-highlight_green%28+1+%29=0.
Look at x-highlight_red%28+%285%2Ax-10%29%2F5+%29-1=0.
Expanded term -1%2F5 by using associative property on %285%2Ax-10%29
It becomes x-highlight_green%28+1%2F5%2A5%2Ax+%29%2Bhighlight_green%28+1%2F5%2A10+%29-1=0.
Look at x-1%2Fhighlight_red%28+5+%29%2Ahighlight_red%28+5+%29%2Ax%2B1%2F5%2A10-1=0.
Factors 5 and 5 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes x-1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+1+%29%2Ax%2B1%2F5%2A10-1=0.
Look at x-highlight_red%28+1+%29%2F1%2Ahighlight_red%28+1+%29%2Ax%2B1%2F5%2A10-1=0.
Multiplied numerator integers
It becomes x-highlight_green%28+1+%29%2F1%2Ax%2B1%2F5%2A10-1=0.
Look at x-1%2F1%2Ax%2B1%2Fhighlight_red%28+5+%29%2Ahighlight_red%28+10+%29-1=0.
Factors 10 and 5 have greatest common factor (GCF) of 5. Reducing fraction.
It becomes x-1%2F1%2Ax%2B1%2Fhighlight_green%28+1+%29%2Ahighlight_green%28+2+%29-1=0.
Look at x-1%2F1%2Ax%2Bhighlight_red%28+1+%29%2F1%2Ahighlight_red%28+2+%29-1=0.
Multiplied numerator integers
It becomes x-1%2F1%2Ax%2Bhighlight_green%28+2+%29%2F1-1=0.
Look at x-1%2F1%2Ax%2Bhighlight_red%28+2%2F1+%29-highlight_red%28+1+%29=0.
Added fractions or integers together
It becomes x-1%2F1%2Ax%2Bhighlight_green%28+1+%29=0.
Look at x-highlight_red%28+1+%29%2Fhighlight_red%28+1+%29%2Ax%2B1=0.
Reduce similar several occurrences of highlight_red%28+1+%29 to
It becomes x-x%2B1=0.
Look at highlight_red%28+x+%29-highlight_red%28+x+%29%2B1=0.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+-x+%29 replacing them with highlight_green%28+%281-1%29%2Ax+%29
It becomes highlight_green%28+%281-1%29%2Ax+%29%2B1=0.
Look at highlight_red%28+%281-1%29%2Ax+%29%2B1=0.
Since highlight_red%28+%281-1%29%2Ax+%29 has zero as a factor, it should be replaced with a zero
Look at 0%2B1=0.
Added fractions or integers together
It becomes 0%2B1=0.
Look at highlight_red%28+0+%29%2B1=0.
Remove extraneous zero highlight_red%28+0+%29
It becomes 1=0.
Result: 1=0

Universal Simplifier and Solver

Welcome to Graphical Universal Mathematical Expression Simplifier and Algebra Solver (GUMESS).
It solves most middle school algebra equations and simplifies expressions, and it SHOWS ALL WORK. It is free to use.

Enter expression to be simplified, or equation to be solved.
I will figure out if what you typed is an equation.

Enter Expression ==>     
Examples: x^2-2x=-1, 3x-x-x+a-a=5, (x^2-1)/(x+1), 2x-(x+x)


Single letter variables only, no functions, xy means x*y, x(x-1) means x*(x-1), sin(x) means s*i*n*(x)


You must use the "*" (star) symbol for all multiplications! x(x+1) is WRONG! It means a function x of x-1. x*(x-1) is right. Use the ^ (caret) for exponentiation. x^2 means x squared. x/2y means x%2F2y
Resources: Simplifier Portal, help with entering simplifier formulas (a must read).


Or, click on any of these examples: 1, 2-1, 2%5E2-4%5E1, %281%29, -%28-1%29, %28%28%28%28x%29%29%29%29-x, -%28-%28-%28-%28-%28x%29%29%29%29%29%2Bx, %28%28%28%28x%29%29%29%29-y%2Ax%2A2%2Fy, %28x%2B1%29%2F%28x%2B1%29, %281%2Bx%29%2F%28x%2B1%29, %281%2Bx%29%2F%282%2A%28x%2B1%29%29, x-x%2Bx, x%2A%28y%2Az%29+-+%28x%2Ay%29%2Az, %28x-1%29%2A%28y-1%29-%28y-1%29%2A%28x-1%29, %28x-1%29%2A%28y-1%29-%28%28y-1%29%2Fx%29%5E%282-1%29%2A%28x-1%29%2Ax, 2%2A2%2A2%5E2%2Ax-x, 1%2F%282%2Bx%2Ay-y%2Ax%5E2%2F%28x%2B0%29%29, x%5E%28y%2Bz%29-x%5E%28z%2By%29, x-x%2F2, x=x, x%2B1=2, 0=5-x-7, %28x%5E2-x-2%29%2F%28%28x%2B1%29%2F%282x%2B2%29%29=0, %28x-1%29%28x-2%29%2F%28x%2B1%29=0, %28x%5E2-x-2%29=0, %28x%5E2-x-2%29%2A%28x%5E2-x-2%29%2F%28x%5E2%2B2%2Ax%2B1%29%2F%28x%5E2-4%2Ax%2B4%29, %28x%5E3-x%29%2Fx=0, %28x-1%29%2Fx=0, %282x%5E4-2%29%2F%28x-1%29=0, x%5E5-x%5E3=0, %28x-3%29%2A%28x%5E6-2x%5E3%2B1%29=0, , x%2A%28x-1%29%28x%2B1%29%2A%28x%5E3%2Bx%29, %28x-1%29%28x%2B1%29-3=0, %28x%5E2-1%29%28x%5E2%2B1%29-15=0, 1%2Fx%5E-1, x%2Fa%5E%28-5%29, x%2Aa%5E%28-5%29, x%5E-1, 2%2F6, 1%2F2-2%2F3, 1%2F2-1, 1%2F2-1%2B1%2F10, 1%2F2%2B2%2F3, 1%2F3%2B0.51, 1%2F3%2B0.5, x-x%2F3, 0.5x-x%2F3, 0.5x-2%2Ax%2F3, 1%2F2%2B1%2F3%2B1%2F6, %282x%2B2y%29%2F2, %28%28-4%2B10%29-%28-2%2B14%29%29%2F2%2A%282%29.
Please write to Igor Chudov, ichudov @ algebra.com, with questions or suggestions.

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This simplifier has been used 37277800 times.