Simplify (y-1)/(y square root of y+1)

$\frac{y - 1}{y \sqrt{y + 1}}$

Multiply $\frac{y - 1}{y \sqrt{y + 1}}$ by $\frac{\sqrt{y + 1}}{\sqrt{y + 1}}$ .

$\frac{y - 1}{y \sqrt{y + 1}} \cdot \frac{\sqrt{y + 1}}{\sqrt{y + 1}}$

Combine and simplify the denominator.

Multiply $\frac{y - 1}{y \sqrt{y + 1}}$ by $\frac{\sqrt{y + 1}}{\sqrt{y + 1}}$ .

$\frac{(y - 1) \sqrt{y + 1}}{y \sqrt{y + 1} \sqrt{y + 1}}$

Move $\sqrt{y + 1}$ .

$\frac{(y - 1) \sqrt{y + 1}}{y (\sqrt{y + 1} \sqrt{y + 1})}$

Raise $\sqrt{y + 1}$ to the power of $1$ .

$\frac{(y - 1) \sqrt{y + 1}}{y ({\sqrt{y + 1}}^{1} \sqrt{y + 1})}$

Raise $\sqrt{y + 1}$ to the power of $1$ .

$\frac{(y - 1) \sqrt{y + 1}}{y ({\sqrt{y + 1}}^{1} {\sqrt{y + 1}}^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{(y - 1) \sqrt{y + 1}}{y {\sqrt{y + 1}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{(y - 1) \sqrt{y + 1}}{y {\sqrt{y + 1}}^{2}}$

Rewrite ${\sqrt{y + 1}}^{2}$ as $y + 1$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y + 1}$ as ${(y + 1)}^{\frac{1}{2}}$ .

$\frac{(y - 1) \sqrt{y + 1}}{y {({(y + 1)}^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{(y - 1) \sqrt{y + 1}}{y {(y + 1)}^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{(y - 1) \sqrt{y + 1}}{y {(y + 1)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(y - 1) \sqrt{y + 1}}{y {(y + 1)}^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{(y - 1) \sqrt{y + 1}}{y {(y + 1)}^{1}}$

Simplify.

$\frac{(y - 1) \sqrt{y + 1}}{y (y + 1)}$

Reorder factors in $\frac{(y - 1) \sqrt{y + 1}}{y (y + 1)}$ .

$\frac{\sqrt{y + 1} (y - 1)}{y (y + 1)}$