Simplify ( square root of b)/( square root of b-3)

$\frac{\sqrt{b}}{\sqrt{b} - 3}$

Step 1

Multiply $\frac{\sqrt{b}}{\sqrt{b} - 3}$ by $\frac{\sqrt{b} + 3}{\sqrt{b} + 3}$ .

$\frac{\sqrt{b}}{\sqrt{b} - 3} \cdot \frac{\sqrt{b} + 3}{\sqrt{b} + 3}$

Step 2

Multiply $\frac{\sqrt{b}}{\sqrt{b} - 3}$ by $\frac{\sqrt{b} + 3}{\sqrt{b} + 3}$ .

$\frac{\sqrt{b} (\sqrt{b} + 3)}{(\sqrt{b} - 3) (\sqrt{b} + 3)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{\sqrt{b} (\sqrt{b} + 3)}{{\sqrt{b}}^{2} + \sqrt{b} \cdot 3 - 3 \sqrt{b} - 9}$

Step 4

Simplify.

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

$\frac{\sqrt{b} (\sqrt{b} + 3)}{{(b^{\frac{1}{2}})}^{2} - 9}$

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

$\frac{\sqrt{b} (\sqrt{b} + 3)}{b^{\frac{1}{2} \cdot 2} - 9}$

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

$\frac{\sqrt{b} (\sqrt{b} + 3)}{b^{\frac{2}{2}} - 9}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{b} (\sqrt{b} + 3)}{b^{\frac{2}{2}} - 9}$

Rewrite the expression.

$\frac{\sqrt{b} (\sqrt{b} + 3)}{b^{1} - 9}$

Simplify.

$\frac{\sqrt{b} (\sqrt{b} + 3)}{b - 9}$

Step 5

Apply the distributive property.

$\frac{\sqrt{b} \sqrt{b} + \sqrt{b} \cdot 3}{b - 9}$

Step 6

Multiply $\sqrt{b} \sqrt{b}$ .

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

$\frac{{\sqrt{b}}^{1} \sqrt{b} + \sqrt{b} \cdot 3}{b - 9}$

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

$\frac{{\sqrt{b}}^{1} {\sqrt{b}}^{1} + \sqrt{b} \cdot 3}{b - 9}$

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

$\frac{{\sqrt{b}}^{1 + 1} + \sqrt{b} \cdot 3}{b - 9}$

Add $1$ and $1$ .

$\frac{{\sqrt{b}}^{2} + \sqrt{b} \cdot 3}{b - 9}$

Step 7

Simplify terms.

Move $3$ to the left of $\sqrt{b}$ .

$\frac{{\sqrt{b}}^{2} + 3 \cdot \sqrt{b}}{b - 9}$

Rewrite ${\sqrt{b}}^{2}$ as $b$ .

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

$\frac{{(b^{\frac{1}{2}})}^{2} + 3 \cdot \sqrt{b}}{b - 9}$

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

$\frac{b^{\frac{1}{2} \cdot 2} + 3 \cdot \sqrt{b}}{b - 9}$

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

$\frac{b^{\frac{2}{2}} + 3 \cdot \sqrt{b}}{b - 9}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{b^{\frac{2}{2}} + 3 \cdot \sqrt{b}}{b - 9}$

Rewrite the expression.

$\frac{b^{1} + 3 \cdot \sqrt{b}}{b - 9}$

Simplify.

$\frac{b + 3 \cdot \sqrt{b}}{b - 9}$

$\frac{b + 3 \sqrt{b}}{b - 9}$

Step 8

Simplify the numerator.

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

$\frac{b + 3 b^{\frac{1}{2}}}{b - 9}$

Factor $b^{\frac{1}{2}}$ out of $b + 3 b^{\frac{1}{2}}$ .

Raise $b$ to the power of $1$ .

$\frac{b^{1} + 3 b^{\frac{1}{2}}}{b - 9}$

Factor $b^{\frac{1}{2}}$ out of $b^{1}$ .

$\frac{b^{\frac{1}{2}} b^{\frac{1}{2}} + 3 b^{\frac{1}{2}}}{b - 9}$

Factor $b^{\frac{1}{2}}$ out of $3 b^{\frac{1}{2}}$ .

$\frac{b^{\frac{1}{2}} b^{\frac{1}{2}} + b^{\frac{1}{2}} \cdot 3}{b - 9}$

Factor $b^{\frac{1}{2}}$ out of $b^{\frac{1}{2}} b^{\frac{1}{2}} + b^{\frac{1}{2}} \cdot 3$ .

$\frac{b^{\frac{1}{2}} (b^{\frac{1}{2}} + 3)}{b - 9}$

Simplify ( square root of b)/( square root of b-3)

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