## anonymous one year ago simplify by multiplying the conjugate (x-5)/((sqrtx+4)-3) and find exact values of tan(7pi/6) please help with the summer work

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1. anonymous

$if ~\it~is~\sqrt{x+4}-3 ?$ $\frac{ x-5 }{ \sqrt{x+4}-3 } \times \frac{ \sqrt{x+4}+3 }{ \sqrt{x+4}+3 }$

2. anonymous

$=\frac{ \left( x-5 \right)\left( \sqrt{x+4}-3 \right) }{ x+4-9 }=?$

3. anonymous

it is +3 not -3

4. anonymous

$\tan \frac{ 7 \pi }{ 6 }=\tan \left( \pi+\frac{ \pi }{ 6 } \right)=\tan \frac{ \pi }{ 6 }=?$

5. anonymous

i got the first one but still little confuse on second one, can you please explain??

6. anonymous

The tangent function is $$\pi$$-periodic. This means that $$\tan(x\pm\pi)=\tan x$$, which allows you to do what @surjithayer suggested.