Simplify 4y(8y+24)^-1

$4 y {(8 y + 24)}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$4 y \frac{1}{8 y + 24}$

Step 2

Factor $8$ out of $8 y + 24$ .

Factor $8$ out of $8 y$ .

$4 y \frac{1}{8 (y) + 24}$

Factor $8$ out of $24$ .

$4 y \frac{1}{8 y + 8 \cdot 3}$

Factor $8$ out of $8 y + 8 \cdot 3$ .

$4 y \frac{1}{8 (y + 3)}$

Step 3

Cancel the common factor of $4$ .

Factor $4$ out of $4 y$ .

$4 (y) \frac{1}{8 (y + 3)}$

Factor $4$ out of $8 (y + 3)$ .

$4 (y) \frac{1}{4 (2 (y + 3))}$

Cancel the common factor.

$4 y \frac{1}{4 (2 (y + 3))}$

Rewrite the expression.

$y \frac{1}{2 (y + 3)}$

Step 4

Combine $y$ and $\frac{1}{2 (y + 3)}$ .

$\frac{y}{2 (y + 3)}$