What is 3/(sqrt(5)-x) ?

The solution to 3/(sqrt(5)-x) is -3/(x-sqrt(5))

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simplify 3/(sqrt(5)-x)

simplify

\frac{3}{5 - x}

- \frac{3}{x - 5}

Solution steps

\frac{3}{5 - x}

Multiply by the conjugate

\frac{5 + x}{5 + x}

= \frac{3 ( 5 + x )}{( 5 - x ) ( 5 + x )}

(5 - x) (5 + x) = 5 - x^{2}

= \frac{3 ( 5 + x )}{5 - x ^{2}}

Factor

- x^{2} + 5 : - (x + 5) (x - 5)

= - \frac{3 ( 5 + x )}{( x + 5 ) ( x - 5 )}

Cancel the common factor:

5 + x

= - \frac{3}{x - 5}

+ 3 x^{2} - 5 x y - 12 y^{2}

x y \times x y

\frac{3}{2} - \frac{3}{1}

\frac{3}{5} \times \frac{2}{4}

\frac{3}{5} \times \frac{2}{7}