Question

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

Answer 1

`(3x3 - 4x2 - 3x - 15)/(x)`
Step 1 :

simplify

`(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