What is the following quotient?

StartFraction 9 + StartRoot 2 EndRoot Over 4 minus StartRoot 7 EndRoot EndFraction
StartFraction 9 StartRoot 7 EndRoot + StartRoot 14 EndRoot Over negative 3 EndFraction
StartFraction 36 minus 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot minus StartRoot 14 EndRoot EndFraction
StartFraction 36 + 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot + StartRoot 14 EndRoot Over 9 EndFraction
StartFraction 79 Over 9 EndFraction

StartFraction 36 + 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot + StartRoot 14 EndRoot Over 9 EndFraction

Step-by-step explanation:

(9 + sqrt(2))/(4 - sqrt(7))

Multiply and divide by 4 + sqrt(7)

[(9 + sqrt(2))(4 + sqrt(7))]/(4² - 7)

[36 + 4sqrt(2) + 9sqrt(7) + sqrt(14)]/9

27 +27 or 27times 2=54

the diffrence is 0

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: