Question

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

Answer 1

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)