How do you find the quotient of (3a)/(a^2+2a+1)div(a-1)/(a+1)?

Aug 7, 2018

$\frac{3 a}{\left(a + 1\right) \left(a - 1\right)}$

Explanation:

$\text{factor the denominator of the fraction on the left}$

$\text{Change division to multiplication and turn the fraction}$
$\text{on the right upside down. Perform any cancelling}$

$= \frac{3 a}{\left(a + 1\right) \cancel{\left(a + 1\right)}} \times \frac{\cancel{\left(a + 1\right)}}{a - 1}$

$= \frac{3 a}{\left(a + 1\right) \left(a - 1\right)} = \frac{3 a}{{a}^{2} - 1}$

Aug 7, 2018

$\frac{3 a}{{a}^{2} - 1}$

Explanation:

$\frac{3 a}{{a}^{2} + 2 a + 1} / \left(\frac{a - 1}{a + 1}\right)$

=$\frac{3 a}{{a}^{2} + 2 a + 1} \cdot \frac{a + 1}{a - 1}$

=$\frac{3 a}{a + 1} ^ 2 \cdot \frac{a + 1}{a - 1}$

=$\frac{3 a}{\left(a + 1\right) \cdot \left(a - 1\right)}$

=$\frac{3 a}{{a}^{2} - 1}$