What is (x-4)/(3-sqrt(x+5)) ?

The solution to (x-4)/(3-sqrt(x+5)) is -sqrt(x+5)-3

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simplify (x-4)/(3-sqrt(x+5))

simplify

\frac{x - 4}{3 - x + 5}

- x + 5 - 3

Solution steps

\frac{x - 4}{3 - x + 5}

Multiply by the conjugate

\frac{3 + x + 5}{3 + x + 5}

= \frac{( x - 4 ) ( 3 + x + 5 )}{( 3 - x + 5 ) ( 3 + x + 5 )}

(3 - x + 5) (3 + x + 5) = - x + 4

= \frac{( x - 4 ) ( 3 + x + 5 )}{- x + 4}

Cancel

\frac{( x - 4 ) ( 3 + x + 5 )}{- x + 4} : - (x + 5 + 3)

= - (x + 5 + 3)

Negate

- (x + 5 + 3) = - x + 5 - 3

= - x + 5 - 3

5 x^{2} + 5 x - 60

\frac{2 x - 4}{2}

2^{3 + 1}

2 x y \cdot x

4 y^{2} - 16

What is (x-4)/(3-sqrt(x+5)) ?
The solution to (x-4)/(3-sqrt(x+5)) is -sqrt(x+5)-3