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Simplify. Write your answer using whole numbers and variables. $\newline$ $\frac{g}{3g^2 - 4g}$

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Simplify rational expressions

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Q. Simplify. Write your answer using whole numbers and variables.

\newline

\frac{g}{3g^2 - 4g}

Identify GCF of denominator: Identify the greatest common factor (GCF) of the terms in the denominator, $3g^2$ and $4g$ . $\newline$ The GCF is $g$ , because both terms are divisible by $g$ .
Factor out GCF from denominator: Factor out the GCF, $g$ , from the denominator. $3g^2 - 4g = g(3g - 4)$
Rewrite expression with factored denominator: Rewrite the original expression with the factored denominator. $\newline$ $(g)/(3g^2 - 4g)$ becomes $(g)/(g(3g - 4))$
Cancel out common factor: Cancel out the common factor of $g$ from the numerator and the denominator. $\frac{g}{g(3g - 4)}$ simplifies to $\frac{1}{3g - 4}$ because $\frac{g}{g} = 1$ .

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