Question

simplify the following expression. assume any factors you cancel are not zero. \\(\dfrac{\dfrac{9}{k + 1} - 1}{\dfrac{6}{k + 1} + 1}\\) note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 0 times. you have unlimited attempts remaining. email instructor

Explanation:

Step1: Simplify numerator

Rewrite 1 as $\frac{k+1}{k+1}$ to combine terms.
$\frac{9}{k+1} - 1 = \frac{9}{k+1} - \frac{k+1}{k+1} = \frac{9 - (k+1)}{k+1} = \frac{8 - k}{k+1}$

Step2: Simplify denominator

Rewrite 1 as $\frac{k+1}{k+1}$ to combine terms.
$\frac{6}{k+1} + 1 = \frac{6}{k+1} + \frac{k+1}{k+1} = \frac{6 + (k+1)}{k+1} = \frac{k+7}{k+1}$

Step3: Divide numerator by denominator

Multiply by reciprocal of denominator.
$\frac{\frac{8 - k}{k+1}}{\frac{k+7}{k+1}} = \frac{8 - k}{k+1} \times \frac{k+1}{k+7}$

Step4: Cancel common factors

Cancel $(k+1)$ (since $k+1
eq 0$).
$\frac{8 - k}{k+7}$

Answer:

$\frac{8 - k}{k+7}$