Let's simplify the algebraic expression step by step:
Given expression:
[tex]\[ \frac{30g^3 + 15g^2}{5g} \][/tex]
Step 1: Factor out the common terms in the numerator.
[tex]\[ 30g^3 + 15g^2 = 15g^2(2g) + 15g^2 = 15g^2(2g + 1) \][/tex]
Step 2: Rewrite the original expression using the factorized form.
[tex]\[ \frac{30g^3 + 15g^2}{5g} = \frac{15g^2(2g + 1)}{5g} \][/tex]
Step 3: Simplify the fraction by dividing the numerator and the denominator by [tex]\(5g\)[/tex].
[tex]\[ \frac{15g^2(2g + 1)}{5g} = \frac{15}{5} \cdot \frac{g^2}{g} \cdot (2g + 1) \][/tex]
Step 4: Perform the division.
[tex]\[ \frac{15}{5} = 3 \][/tex]
[tex]\[ \frac{g^2}{g} = g \][/tex]
So,
[tex]\[ 3 \cdot g \cdot (2g + 1) = 3g(2g + 1) \][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[ 3g(2g + 1) \][/tex]
