Question

simplify each of the following fractions 1a)2/x4 1b)3x+9/x+5 1c) 14x^3-x^2+9x-2/x^2-16 1d)3x/6x^2-x-2

Answer 1

step  1  : 6 Simplify —— x2 Equation at the end of step  1  : 10 6 (((((x2)+3x)-————)-2x)-15)——)+6x)+9) (x2)(((((x^2)x2 Step  2  :Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole 

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

x2 + x (x2 + x) • x2 x2 + x = —————— = ————————————— 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 + x  =   x • (x + 1) 

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+1) • x2 - (6) x4 + x3 - 6 ———————————————————— = ——————————— x2 x2 Equation at the end of step  3  : 10 (x4+x3-6) (((((x2)+3x)-————)-2x)-15)—————————+6x)+9) (x2)(( 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