Simplify the expression and solve the equation. show all calculations

First of all, we can observe that

Then, we can rationalize the denominator by using the formula

If we multiply both numerator and denominator by [/tex]\sqrt{8}+3[/tex] we have

We can also observe that

And the expression simplifies into

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.