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# Recent problems solved by 'ikleyn'

 Numeric_Fractions/479514: if a,b,c and d are in set of natural numbers(N) with a=bcd, b=cda and d=abc then,what is the value of (a+b+c+d)^2 ? 1 solutions Answer 328557 by ikleyn(4)   on 2011-08-09 00:30:07 (Show Source): You can put this solution on YOUR website!Since and , we can substitute b into the first equation and obtain , which can be simplified into . Since a,b,c,d are natural numbers (not equal to zero), we can divide both sides of the last equation by a and obtain . Again, using the fact that a,b,c,d are natural numbers we conclude that both c and d are equal to 1. Now we have to find values of a and b. We can use the last equation and substitute c = 1 and d = 1 to obtain . Again, a and b are natural numbers, and thus both equal to 1. So, the only solution to the system of equations for a,b,c,d among the set of natural numbers is all of the being equal to 1. Thus is equal to 16.
Rational-functions/478039: Simplify the rational expression
3x^2-7x+4/5x^2-8x+3
1 solutions

Answer 327581 by ikleyn(4)   on 2011-08-04 22:35:07 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: Graphical form: simplifies to Text form: (3x^2-7x+4)/(5x^2-8x+3) simplifies to (3*x-4)/(5*x-3)Cartoon (animation) form: For tutors: `simplify_cartoon( (3x^2-7x+4)/(5x^2-8x+3) )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Canceled out common factors (x-(1))
Result:

### Universal Simplifier and Solver

Done!

test/444960: 2-10x=(3x-7)(x+1)
1 solutions

Answer 306623 by ikleyn(4)   on 2011-05-04 13:26:27 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=-3,x=1. Graphical form: Equation was fully solved.Text form: 2-10x=(3x-7)*(x+1) simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 2-10x=(3x-7)*(x+1) )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved to the right of expression
It becomes .

Look at .
Moved these terms to the left
It becomes .

Look at .
Moved to the right of expression
It becomes .

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
Reduce similar several occurrences of to
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Expanded term by using associative property on
It becomes .

Look at .
Multiplied numerator integers
It becomes .

Look at .
It becomes .

Look at .
Eliminated similar terms , replacing them with
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Equation is a quadratic equation: -3*x^2-6*x+9 =0, and has solutions -3,1
It becomes .
Result:
This is an equation! Solutions: x=-3,x=1.

### Universal Simplifier and Solver

Done!

Equations/444963: solve this equation 2/3x=5/6
1 solutions

Answer 306620 by ikleyn(4)   on 2011-05-04 13:21:17 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=1.25. Graphical form: Equation was fully solved.Text form: 2/3*x=5/6 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( 2/3*x=5/6 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Moved these terms to the left
It becomes .

Look at .
Solved linear equation equivalent to 0.666666666666667*x-0.833333333333333 =0
It becomes .
Result:
This is an equation! Solutions: x=1.25.

Done!