Divide. Write your answer in simplest form. v - 5/5v - 1 ÷ (5v^2 - 26v + 5) ______

Rewrite as multiplication: Rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction. (v - 5)/(5v - 1) ÷ (5v^2 - 26v + 5) can be rewritten as (v - 5)/(5v - 1) × 1/(5v^2 - 26v + 5).Factor quadratic expression: Factor the quadratic expression in the denominator of the second fraction if possible. 5v^2 - 26v + 5 can be factored into (5v - 1)(v - 5).Use factored form: Rewrite the expression using the factored form of the denominator. The expression now becomes (v - 5)/(5v - 1) × 1/((5v - 1)(v - 5)).Multiply numerators and denominators: Multiply the numerators and the denominators. (v - 5)/(5v - 1) × 1/((5v - 1)(v - 5)) = (v - 5) * 1 / ((5v - 1)(v - 5)).Cancel common factors: Cancel out the common factors in the numerator and the denominator. The (v - 5) terms cancel out, as do the (5v - 1) terms, leaving us with 1/1.Simplify expression: Simplify the expression. 1/1 simplifies to just 1.

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Algebra 2

Multiply and divide rational expressions

Full solution

Q. Divide. Write your answer in simplest form.

\newline

\frac{v - 5}{5v - 1} \div (5v^2 - 26v + 5)

Rewrite as multiplication: Rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction. $\newline$ $(v - 5)/(5v - 1) \div (5v^2 - 26v + 5)$ can be rewritten as $(v - 5)/(5v - 1) \times 1/(5v^2 - 26v + 5)$ .
Factor quadratic expression: Factor the quadratic expression in the denominator of the second fraction if possible. $\newline$ $5v^2 - 26v + 5$ can be factored into $(5v - 1)(v - 5)$ .
Use factored form: Rewrite the expression using the factored form of the denominator. The expression now becomes $(v - 5)/(5v - 1) \times 1/((5v - 1)(v - 5))$ .
Multiply numerators and denominators: Multiply the numerators and the denominators. $\newline$ $(v - 5)/(5v - 1) \times 1/((5v - 1)(v - 5)) = (v - 5) \times 1 / ((5v - 1)(v - 5))$ .
Cancel common factors: Cancel out the common factors in the numerator and the denominator. $\newline$ The $(v - 5)$ terms cancel out, as do the $(5v - 1)$ terms, leaving us with $\frac{1}{1}$ .
Simplify expression: Simplify the expression. $\frac{1}{1}$ simplifies to just $1$ .