Divide. Write your answer in simplest form. v - 5/35v + 14 ÷ v - 5/7 ______

Rewrite as multiplication problem: Write the division problem as a multiplication problem by taking the reciprocal of the second fraction. (v - 5)/(35v + 14) ÷ (v - 5)/7 can be rewritten as (v - 5)/(35v + 14) × 7/(v - 5).Factor out common factor: Factor out the common factor in the denominator of the first fraction. 35v + 14 can be factored as 7(5v + 2) because 35v = 7 * 5v and 14 = 7 * 2. So, the first fraction becomes (v - 5)/(7(5v + 2)).Multiply numerators and denominators: Multiply the numerators and the denominators of the fractions. (v - 5)/(7(5v + 2)) × 7/(v - 5) = (v - 5) * 7 / (7(5v + 2) * (v - 5)).Cancel out common factors: Cancel out the common factors in the numerator and the denominator. The (v - 5) terms cancel out, and one of the 7's cancels out, leaving us with: 1 / (5v + 2).Check for simplest form: Check that the expression is in its simplest form. There are no common factors left in the numerator and the denominator, and the expression cannot be simplified further.

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Algebra 2

Multiply and divide rational expressions

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Q. Divide. Write your answer in simplest form.

\newline

\frac{v - 5}{35v + 14} \div \frac{v - 5}{7}

Rewrite as multiplication problem: Write the division problem as a multiplication problem by taking the reciprocal of the second fraction. $\newline$ $(v - 5)/(35v + 14) \div (v - 5)/7$ can be rewritten as $(v - 5)/(35v + 14) \times 7/(v - 5)$ .
Factor out common factor: Factor out the common factor in the denominator of the first fraction. $\newline$ $35v + 14$ can be factored as $7(5v + 2)$ because $35v = 7 \times 5v$ and $14 = 7 \times 2$ . $\newline$ So, the first fraction becomes $(v - 5)/(7(5v + 2))$ .
Multiply numerators and denominators: Multiply the numerators and the denominators of the fractions. $\newline$ (v - \(5)/( $7$ ( $5$ v + $2$ )) \times $7$ /(v - $5$ ) = (v - $5$ ) \times $7$ / ( $7$ ( $5$ v + $2$ ) \times (v - $5$ )).
Cancel out common factors: Cancel out the common factors in the numerator and the denominator. $\newline$ The $(v - 5)$ terms cancel out, and one of the $7$ 's cancels out, leaving us with: $\newline$ $\frac{1}{5v + 2}$ .
Check for simplest form: Check that the expression is in its simplest form. $\newline$ There are no common factors left in the numerator and the denominator, and the expression cannot be simplified further.