What is (2x-sqrt(3x))/(2x+sqrt(3x)) ?

The solution to (2x-sqrt(3x))/(2x+sqrt(3x)) is ((2sqrt(x)-sqrt(3))^2)/(4x-3)

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simplify (2x-sqrt(3x))/(2x+sqrt(3x))

simplify

\frac{2 x - 3 x}{2 x + 3 x}

\frac{( 2 x - 3 ) ^{2}}{4 x - 3}

Solution steps

\frac{2 x - 3 x}{2 x + 3 x}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{2 x - 3 x}{2 x + 3 x}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{2 x - 3 x}{2 x + 3 x}

Factor

2 x - 3 x : x (2 x - 3)

= \frac{x ( 2 x - 3 )}{2 x + 3 x}

Factor

2 x + 3 x : x (2 x + 3)

= \frac{x ( 2 x - 3 )}{x ( 2 x + 3 )}

Cancel the common factor:

x

= \frac{2 x - 3}{2 x + 3}

Rationalize

\frac{2 x - 3}{2 x + 3} : \frac{( 2 x - 3 ) ^{2}}{4 x - 3}

= \frac{( 2 x - 3 ) ^{2}}{4 x - 3}

2 \frac{4}{6} \div \frac{1}{6}

\frac{3}{2} + \frac{2}{2}

\frac{x ^{2} y ^{2} z ^{2}}{4 y ^{4}}

(x - \frac{4}{3})^{2}

w^{2} + 10 w + 25

What is (2x-sqrt(3x))/(2x+sqrt(3x)) ?
The solution to (2x-sqrt(3x))/(2x+sqrt(3x)) is ((2sqrt(x)-sqrt(3))^2)/(4x-3)