Simplify the expression (6a^2+12a)/(3a^2b-6ab^3) | SnapXam

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 Exercise

$\frac{6a^2+12a}{3a^2b-6ab^3}$

 Step-by-step Solution

 

1

Factor the polynomial $6a^2+12a$ by it's greatest common factor (GCF): $6a$

$\frac{6a\left(a+2\right)}{3a^2b-6ab^3}$

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2

Factor the polynomial $3a^2b-6ab^3$ by it's greatest common factor (GCF): $3ab$

$\frac{6a\left(a+2\right)}{3ab\left(a-2b^2\right)}$

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3

Simplify the fraction $\frac{6a\left(a+2\right)}{3ab\left(a-2b^2\right)}$ by $a$

$\frac{6\left(a+2\right)}{3b\left(a-2b^2\right)}$

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4

Cancel the fraction's common factor $3$

$\frac{2\left(a+2\right)}{b\left(a-2b^2\right)}$

Final answer to the exercise  

$\frac{2\left(a+2\right)}{b\left(a-2b^2\right)}$

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 Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

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