Divide. Simplify your answer. 17s/18s^2u^2 ÷ 16u ______

Rewrite Division: Rewrite the division as a multiplication by taking the reciprocal of the divisor. So, (17s/18s^2u^2) ÷ (16u) becomes (17s/18s^2u^2) × (1/16u).Multiply Numerators: Multiply the numerators and then multiply the denominators. So, (17s/18s^2u^2) × (1/16u) becomes (17s × 1) / (18s^2u^2 × 16u).Cancel Common Factors: Simplify the expression by canceling out common factors. The s in the numerator and one s in the denominator cancel out, and u in the denominator cancels out with u in the numerator. So, (17 × 1) / (18s × 16u^2) becomes 17 / (18 × 16s × u^2).Simplify Denominators: Simplify the constants in the denominator by multiplying them. So, 18 × 16 becomes 288. The expression now is 17 / (288s × u^2).Final Simplification: Write the answer in the simplest form. The expression 17 / (288s × u^2) is already in its simplest form since 17 and 288 have no common factors other than 1.

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Math Problems

Algebra 1

Multiply and divide rational expressions

Full solution

Q. Divide. Simplify your answer.

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\frac{17s}{18s^2u^2} \div 16u

Rewrite Division: Rewrite the division as a multiplication by taking the reciprocal of the divisor. So, $(\frac{17s}{18s^2u^2}) \div (16u)$ becomes $(\frac{17s}{18s^2u^2}) \times (\frac{1}{16u})$ .
Multiply Numerators: Multiply the numerators and then multiply the denominators. So, $(\frac{17s}{18s^2u^2}) \times (\frac{1}{16u})$ becomes $(\frac{17s \times 1}{18s^2u^2 \times 16u})$ .
Cancel Common Factors: Simplify the expression by canceling out common factors. The $s$ in the numerator and one $s$ in the denominator cancel out, and $u$ in the denominator cancels out with $u$ in the numerator. So, $(17 \times 1) / (18s \times 16u^2)$ becomes $17 / (18 \times 16s \times u^2)$ .
Simplify Denominators: Simplify the constants in the denominator by multiplying them. So, $18 \times 16$ becomes $288$ . The expression now is $\frac{17}{288s \times u^2}$ .
Final Simplification: Write the answer in the simplest form. The expression $\frac{17}{288s \times u^2}$ is already in its simplest form since $17$ and $288$ have no common factors other than $1$ .