How do you simplify $\frac { \sqrt { x - 5} } { 3} - \frac { 2} { \sqrt { x - 5} }$ ?

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Answer 1 · 2017-08-15T09:02:13

$((x - 11) (sqrt (x - 5)))/(3(x - 5)$

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

Taking L.C.M

$rArr ((sqrt (x - 5)) (sqrt (x - 5)) - ( 2 xx 3))/((3) sqrt (x - 5))$

$rArr (sqrt ((x - 5))^2 - 6)/(3sqrt (x - 5))$

$rArr (x - 5 - 6)/(3sqrt (x - 5))$

$rArr (x - 11)/(3sqrt (x - 5))$

$rArr (x - 11)/(3sqrt (x - 5)) xx (sqrt (x - 5))/(sqrt (x - 5))$

$rArr ((x - 11) (sqrt (x - 5)))/(3sqrt (x - 5)^2$

$rArr ((x - 11) (sqrt (x - 5)))/(3 xx (x - 5)$

$rArr ((x - 11) (sqrt (x - 5)))/(3(x - 5)$

Answer 2 · 2017-08-15T10:01:32

$=(x-5 -6sqrt(x-5))/(3(x-5))$

Before we subtract the fractions, let's change the second one so there is no radical in the denominator.

$sqrt(x-5)/3 - 2/sqrt(x-5) xx sqrt(x-5)/sqrt(x-5)color(white)(xxxxx)color(blue)([ sqrt(x-5)/sqrt(x-5) =1]$

$=sqrt(x-5)/3 - (2sqrt(x-5))/((x-5))" "larr (sqrt(x-5)^2 = (x-5))$

$=(sqrt(x-5)sqrt(x-5)" " -" " 3xx2sqrt(x-5))/(3(x-5)$

$=(x-5 -6sqrt(x-5))/(3(x-5))$

How do you simplify \frac { \sqrt { x - 5} } { 3} - \frac { 2} { \sqrt { x - 5} }\frac { \sqrt { x - 5} } { 3} - \frac { 2} { \sqrt { x - 5} }?