Question

3/4 + 4/13 divided 3/52 -6 simplification​

Answer 1

Answer:

Step  1  :

52 Simplify —— x3

Equation at the end of step  1  :

52 (—— + 21) - 60 = 0 x3

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a whole to a fraction 

Rewrite the whole as a fraction using  x3  as the denominator :

21 21 • x3 21 = —— = ——————— 1 x3

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 denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

52 + 21 • x3 21x3 + 52 ———————————— = ————————— x3 x3

Equation at the end of step  2  :

(21x3 + 52) ——————————— - 60 = 0 x3

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction 

Rewrite the whole as a fraction using  x3  as the denominator :

60 60 • x3 60 = —— = ——————— 1 x3

Trying to factor as a Sum of Cubes :

 3.2      Factoring:  21x3 + 52 

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+b3

Check :  21  is not a cube !!