Question

**CONJUGATES**

Rationalize the denominator and simplify.

(SCREENSHOT)

Answer 1

5/4-sqrt3 *4+sqrt3/4+sqrt3 so its 5*(4+sqrt3)/4-(sqrt3)*4+sqrt3). 20+5sqrt3/16-3 = (20+5sqrt3)/13. Hope this helps u

Answer 2

To rationalize the denominator, we have to multiply by the conjugate

the conjugate for a+b is a-b
the conjugate for a-b is a+b

You just switch that sign in the middle

Answer 3

So what is the conjugate of \( 4 - \sqrt{3}\)

Answer 4

uh \[4+\sqrt{3}\] ?

Answer 5

Good!

Now we have to multiply both the numerator and denominator by the conjugate. You have to do it to both the numerator and denominator to keep it balanced. It's basically like multiplying by 1 so we're not changing anything but we're able to simplify it.

\(\dfrac{5}{4-\sqrt{3}} \times \dfrac{4+\sqrt{3}}{4 + \sqrt{3}} = ?\)

remember this formula

(a-b)(a+b) = a^2 - b^2

Answer 6

ok

Answer 7

i got

Answer 8

where did that x come from?
otherwise, it would be fine

Answer 9

i accidently added x to the question oops

Answer 10

Just remove it and you're good to go! Well done!

Answer 11

thank you !

Answer 12

My pleasure! :)