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

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

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

simplify

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

- x + 4 - 3

Solution steps

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

Multiply by the conjugate

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

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

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

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

Cancel

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

= - (x + 4 + 3)

Negate

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

= - x + 4 - 3

x (x - 3) + 4 (x - 3)

\frac{2}{3} \div 9

(38)^{2}

343 - y^{6}

\frac{3 + 2 i}{4 - 5 i}

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