Eh this is semi hard. explain your thought process/work when done! !

Hello from MrBillDoesMath!

x =2, y= 3, z = 1

Discussion:

Applying the Pythagorean thereon to the leftmost triangle gives:

y^2 + (sqrt(3))^2 =  (sqrt(12) ) ^2     =>

y^2 + 3                = 12                     => subtract 3 from both sides

y^2                      = 12 - 3 = 9          => take square root of both sides

y =   3

In the full triangle, based on similar triangles, we have

(y + z) /  (sqrt(12)) =  sqrt(12)/y   =>  multiply both sides by sqrt(12)

(y + z) =  (sqrt(12)^2 /y               =>   multiply both sides by y

y(y+z) = 12                                  =>  y = 3. Substitute.

3 (3 + z) = 12                              => divide both sides by 4

(3+z) = 12/3 =4                            => subtract 3 from both sides

z = 4 -3 = 1

Finally, using Pythagoras in the small rightmost triangle gives

x^2 = ((sqrt(3))^2 + z^2             => simplify

x^2 = 3 + z^2                            => but z = 1 from above. Substitute

x^2 = 3 + 1^2 = 4                       => take square roots of both sides

x = sqrt(4) = 2

Conclusion: x =2, y= 3, z = 1

Thank you,

MrB

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b