Yvaries directly as x. y = 42 when x= 3 find y when x = 11

Simplify   ——

           x2

Equation at the end of step

1

:

                    3            

 x2) +  4x) +  ——) +  6x) -  9

                   x2            

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Adding a fraction to a whole

Rewrite the whole as a fraction using  x2  as the denominator :

               x2 + 4x     (x2 + 4x) • x2

    x2 + 4x =  ———————  =  ——————————————

                  1              x2      

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

3

:

Pulling out like terms

3.1     Pull out like factors :

  x2 + 4x  =   x • (x + 4)  

Adding fractions that have a common denominator :

3.2       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:

x • (x+4) • x2 + 3     x4 + 4x3 + 3

——————————————————  =  ————————————

        x2                  x2      

Equation at the end of step

3

:

  (x4 + 4x3 + 3)            

 (—————————————— +  6x) -  9

      3  x2                  

STEP

4

:

Rewriting the whole as an Equivalent Fraction :

4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  x2  as the denominator :

         6x     6x • x2

   6x =  ——  =  ———————

         1        x2