Verified answer

To simplify you are trying to get rid of all radicals in the denominator

7/(4-√3), multiply the whole fraction by 4+√3, this creates difference of squares in the denominator

(7/(4-√3)((4+√3)/(4+v3) = (28+7√3)/(16-3) = (28 + 7√3)/15

(28 + 7√3)/15, that should be your answer

To simplify completely you will need to rationalise the denominator (meaning to get rid of all the radicals in the denominator). In this case you will need to multiply both the numerator and denominator by the denominators opposite (4 + √3):

7(4 + √3) = 28 + 7√3

(4 - √3) (4 + √3) = 16 - 3 = 13

Return those values back to the fraction:

(28 + 7√3) / (13)

7 / (4 - √3)

= 7 / (4 - √3 ) X ( 4 + √3 ) / ( 4 + √3 ) because ( 4 + √3 ) / ( 4 + √3 ) = 1

so it's basically 7 / ( 4 - √3 ) x 1

You want to get rid of the surds in the denominator following this rule :

( x + y ) ( x - y ) = x^2 - y^2 , with x being 4 and y being √3

so the denominator will no longer have a surd √ and only the numerator will.

7/(4-√3)=

[7/(4-√3)]*(4+√3)=

7(4+√3)/(4-√3)(4+√3)=

7(4+√3)/(4^2-√3^2)=

(28+7√3)/(16-3)=

(28+7√3)/13.

This is not a simplification, but a rationalization.

Move your *** and learn some maths!

1. remove the radical from the bottom so multiply top & bottom by the opposite:

[7][4+√3] / [4-√3] [4+√3]

2. top becomes: 28 + √3

3. FOIL bottom to get:[4][4]+[4][√3] + [4][-√3] + [-√3][√3] = 16-3 = 13 (the 2 middle terms cancel out)

4. answer becomes : [28 + √3] / [13]