Simplify (2 square root of x-3 square root of y)/( square root of x+ square root of y)

$\frac{2 \sqrt{x} - 3 \sqrt{y}}{\sqrt{x} + \sqrt{y}}$

Multiply $\frac{2 \sqrt{x} - 3 \sqrt{y}}{\sqrt{x} + \sqrt{y}}$ by $\frac{\sqrt{x} - \sqrt{y}}{\sqrt{x} - \sqrt{y}}$ .

$\frac{2 \sqrt{x} - 3 \sqrt{y}}{\sqrt{x} + \sqrt{y}} \cdot \frac{\sqrt{x} - \sqrt{y}}{\sqrt{x} - \sqrt{y}}$

Combine fractions.

Multiply $\frac{2 \sqrt{x} - 3 \sqrt{y}}{\sqrt{x} + \sqrt{y}}$ by $\frac{\sqrt{x} - \sqrt{y}}{\sqrt{x} - \sqrt{y}}$ .

$\frac{(2 \sqrt{x} - 3 \sqrt{y}) (\sqrt{x} - \sqrt{y})}{(\sqrt{x} + \sqrt{y}) (\sqrt{x} - \sqrt{y})}$

Expand the denominator using the FOIL method.

$\frac{(2 \sqrt{x} - 3 \sqrt{y}) (\sqrt{x} - \sqrt{y})}{{\sqrt{x}}^{2} - \sqrt{x y} + \sqrt{y x} - {\sqrt{y}}^{2}}$

Simplify.

$\frac{(2 \sqrt{x} - 3 \sqrt{y}) (\sqrt{x} - \sqrt{y})}{x - y}$

Expand $(2 \sqrt{x} - 3 \sqrt{y}) (\sqrt{x} - \sqrt{y})$ using the FOIL Method.

Apply the distributive property.

$\frac{2 \sqrt{x} (\sqrt{x} - \sqrt{y}) - 3 \sqrt{y} (\sqrt{x} - \sqrt{y})}{x - y}$

Apply the distributive property.

$\frac{2 \sqrt{x} \sqrt{x} + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} (\sqrt{x} - \sqrt{y})}{x - y}$

Apply the distributive property.

$\frac{2 \sqrt{x} \sqrt{x} + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

Simplify and combine like terms.

Simplify each term.

Multiply $2 \sqrt{x} \sqrt{x}$ .

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

$\frac{2 ({\sqrt{x}}^{1} \sqrt{x}) + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

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

$\frac{2 ({\sqrt{x}}^{1} {\sqrt{x}}^{1}) + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

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

$\frac{2 {\sqrt{x}}^{1 + 1} + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

Add $1$ and $1$ .

$\frac{2 {\sqrt{x}}^{2} + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

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

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

$\frac{2 {(x^{\frac{1}{2}})}^{2} + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

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

$\frac{2 x^{\frac{1}{2} \cdot 2} + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

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

$\frac{2 x^{\frac{2}{2}} + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{\frac{2}{2}} + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

Rewrite the expression.

$\frac{2 x^{1} + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

Simplify.

$\frac{2 x + 2 \sqrt{x} (- \sqrt{y}) - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

Multiply $2 \sqrt{x} (- \sqrt{y})$ .

Multiply $- 1$ by $2$ .

$\frac{2 x - 2 \sqrt{x} \sqrt{y} - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

Combine using the product rule for radicals.

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{y} \sqrt{x} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

Combine using the product rule for radicals.

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} - 3 \sqrt{y} (- \sqrt{y})}{x - y}$

Multiply $- 3 \sqrt{y} (- \sqrt{y})$ .

Multiply $- 1$ by $- 3$ .

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 \sqrt{y} \sqrt{y}}{x - y}$

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

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 ({\sqrt{y}}^{1} \sqrt{y})}{x - y}$

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

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 ({\sqrt{y}}^{1} {\sqrt{y}}^{1})}{x - y}$

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

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 {\sqrt{y}}^{1 + 1}}{x - y}$

Add $1$ and $1$ .

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 {\sqrt{y}}^{2}}{x - y}$

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

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

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 {(y^{\frac{1}{2}})}^{2}}{x - y}$

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

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 y^{\frac{1}{2} \cdot 2}}{x - y}$

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

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 y^{\frac{2}{2}}}{x - y}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 y^{\frac{2}{2}}}{x - y}$

Rewrite the expression.

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 y^{1}}{x - y}$

Simplify.

$\frac{2 x - 2 \sqrt{y x} - 3 \sqrt{x y} + 3 y}{x - y}$

Subtract $3 \sqrt{x y}$ from $- 2 \sqrt{y x}$ .

Reorder $y$ and $x$ .

$\frac{2 x - 2 \sqrt{x y} - 3 \sqrt{x y} + 3 y}{x - y}$

Subtract $3 \sqrt{x y}$ from $- 2 \sqrt{x y}$ .

$\frac{2 x - 5 \sqrt{x y} + 3 y}{x - y}$

Simplify (2 square root of x-3 square root of y)/( square root of x+ square root of y)

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