Reducing Fractions To Their Lowest Terms - Tiger Algebra

Step 1 :

Equation at the end of step 1 :

Step 2 :

Equation at the end of step 2 :

Step 3 :

Equation at the end of step 3 :

Step 4 :

Equation at the end of step 4 :

Step 5 :

Rewriting the whole as an Equivalent Fraction :

5.1 Adding a fraction to a whole Rewrite the whole as a fraction using 2 as the denominator :

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

Step 6 :

Pulling out like terms :

6.1 Pull out like factors : 2x2 - 9x = x • (2x - 9)

Adding fractions that have a common denominator :

6.2 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:

Equation at the end of step 6 :

Step 7 :

Rewriting the whole as an Equivalent Fraction :

7.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using 2 as the denominator :

Step 8 :

Pulling out like terms :

8.1 Pull out like factors : 9x3 + 4x2 - 18x = x • (9x2 + 4x - 18)

Trying to factor by splitting the middle term

8.2 Factoring 9x2 + 4x - 18 The first term is, 9x2 its coefficient is 9 .The middle term is, +4x its coefficient is 4 .The last term, "the constant", is -18 Step-1 : Multiply the coefficient of the first term by the constant 9 • -18 = -162 Step-2 : Find two factors of -162 whose sum equals the coefficient of the middle term, which is 4 .

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored

Adding fractions that have a common denominator :

8.3 Adding up the two equivalent fractions

Equation at the end of step 8 :

Step 9 :

Dividing exponential expressions :

9.1 x1 divided by x2 = x(1 - 2) = x(-1) = 1/x1 = 1/x

Equation at the end of step 9 :

Step 10 :

Equation at the end of step 10 :

Step 11 :

Rewriting the whole as an Equivalent Fraction :

11.1 Adding a fraction to a whole Rewrite the whole as a fraction using x as the denominator :

Adding fractions that have a common denominator :

11.2 Adding up the two equivalent fractions

Equation at the end of step 11 :

Step 12 :

Rewriting the whole as an Equivalent Fraction :

12.1 Subtracting a whole from a fraction Rewrite the whole as a fraction using x as the denominator :

Step 13 :

Pulling out like terms :

13.1 Pull out like factors : 3x3 + 9 = 3 • (x3 + 3)

Trying to factor as a Sum of Cubes :

13.2 Factoring: x3 + 3 Theory : A sum 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 : 3 is not a cube !! Ruling : Binomial can not be factored as the difference of two perfect cubes

Polynomial Roots Calculator :

13.3 Find roots (zeroes) of : F(x) = x3 + 3Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x 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 3. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,3 Let us test ....

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

13.4 Adding up the two equivalent fractions

Equation at the end of step 13 :

Step 14 :

Step 15 :

Pulling out like terms :

15.1 Pull out like factors : 3x3 - 9x + 9 = 3 • (x3 - 3x + 3)

Step 16 :

Pulling out like terms :

16.1 Pull out like factors : (9x3 - 2x2 - 18x) = x • (9x2 - 2x - 18)

Polynomial Roots Calculator :

16.2 Find roots (zeroes) of : F(x) = x3 - 3x + 3 See theory in step 13.3 In this case, the Leading Coefficient is 1 and the Trailing Constant is 3. The factor(s) are: of the Leading Coefficient : 1 of the Trailing Constant : 1 ,3 Let us test ....

Polynomial Roots Calculator found no rational roots

Trying to factor by splitting the middle term

16.3 Factoring 9x2 - 2x - 18 The first term is, 9x2 its coefficient is 9 .The middle term is, -2x its coefficient is -2 .The last term, "the constant", is -18 Step-1 : Multiply the coefficient of the first term by the constant 9 • -18 = -162 Step-2 : Find two factors of -162 whose sum equals the coefficient of the middle term, which is -2 .

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored

Final result :