Solve Reducingfractionstolowestterms C-5/c2-25 Tiger Algebra Solver

Reformatting the input :

Changes made to your input should not affect the solution: (1): "c2" was replaced by "c^2".

Step 1 :

5 Simplify —— c2

Equation at the end of step 1 :

5 (c - ——) - 25 c2

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a fraction from a whole Rewrite the whole as a fraction using c2 as the denominator :

c c • c2 c = — = —————— 1 c2

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

c • c2 - (5) c3 - 5 ———————————— = —————— c2 c2

Equation at the end of step 2 :

(c3 - 5) ———————— - 25 c2

Step 3 :

Rewriting the whole as an Equivalent Fraction :

3.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using c2 as the denominator :

25 25 • c2 25 = —— = ——————— 1 c2

Trying to factor as a Difference of Cubes:

3.2 Factoring: c3 - 5 Theory : A difference of two perfect cubes, a3 - b3 can be factored into (a-b) • (a2 +ab +b2)Proof : (a-b)•(a2+ab+b2) = a3+a2b+ab2-ba2-b2a-b3 = a3+(a2b-ba2)+(ab2-b2a)-b3 = a3+0+0-b3 = a3-b3Check : 5 is not a cube !! Ruling : Binomial can not be factored as the difference of two perfect cubes

Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(c) = c3 - 5Polynomial Roots Calculator is a set of methods aimed at finding values of c for which F(c)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers c which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 and the Trailing Constant is -5. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,5 Let us test ....

P	Q	P/Q	F(P/Q)	Divisor
-1	1	-1.00	-6.00
-5	1	-5.00	-130.00
1	1	1.00	-4.00
5	1	5.00	120.00

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

3.4 Adding up the two equivalent fractions

(c3-5) - (25 • c2) c3 - 25c2 - 5 —————————————————— = ————————————— c2 c2

Polynomial Roots Calculator :

3.5 Find roots (zeroes) of : F(c) = c3 - 25c2 - 5 See theory in step 3.3 In this case, the Leading Coefficient is 1 and the Trailing Constant is -5. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,5 Let us test ....

P	Q	P/Q	F(P/Q)	Divisor
-1	1	-1.00	-31.00
-5	1	-5.00	-755.00
1	1	1.00	-29.00
5	1	5.00	-505.00

Polynomial Roots Calculator found no rational roots

Final result :

c3 25c2 - 5 ————————————— c2