Find limit as x approaches 4 of the quotient of the quantity the square root of the quantity 3 times x plus 4 minus the square root of 4 times x and the quantity x squared minus 4 times x. you must show your work or explain your work in words

Lim x-4 (√3x+4 - √4x) / (x^2-4x) simplify √4x to equal 2√x

multiply by the conjugate (√3x+4 - 2√x) (√3x+4 + 2√x) / (x^2-4x) (√3x+4 + 2√x)

simplify = - x+4 / (x^2-4x) (√3x+4 + 2√x)

factor (x^2-4x) which equals x (x-4)

-x+4 / x (x-4) (√3x+4 + 2√x)

simplify = - 1 / 4 (√3x+4 + 2√x)

next plug in 4

-1 / 4 (√3 (4) + 4 + 2 √ (4)) = (-1/32)