Question

What is the quotient (3x^2 + 4x-15) divided by (x+3)

Answer 1

$\frac{3x3 - 4x2 - 3x - 15}{x}$
Step  1  :

simplify
$\frac{15}{x}$
Equation at the end of step  1  :

15 (((3 • (x2)) - 4x) - ——) - 3 x

Step  2  :

Equation at the end of step  2  :

15 ((3x2 - 4x) - ——) - 3 x

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole 

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

3x2 - 4x (3x2 - 4x) • x 3x2 - 4x = ———————— = —————————————— 1 x

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  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   3x2 - 4x  =   x • (3x - 4) 

Adding fractions that have a common denominator :

 4.2       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 • (3x-4) • x - (15) 3x3 - 4x2 - 15 ————————————————————— = —————————————— x x

Equation at the end of step  4  :

(3x3 - 4x2 - 15) ———————————————— - 3 x

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction 

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

3 3 • x 3 = — = ————— 1 x