Limits question can someone please help me

limit as x approaches 4 (4-x) / (4- 2sqrt(x))
struggling with question need to find answer without using L'hospital rule I know the answer is 2 but i can't figure out how to get there... please help me

Need to multiply by conjugate of denominator:

(4-x)(4+2√x) / (4 - 2√x)(4+2√x)

(4-x)(4+2√x) / (16 - 4x)

(4-x)(4+2√x) / (4)(4-x)

Cancel a 4-x

youre left with:
(4+2√x) / 4

Then you plug in 4:
4 + 2√4 / 4

4 + 4 / 4 = 2

Make sure to write limx-->4 on every part til you plug in limit, otherwise teach will deduct points.

Rationalize the denominator,


= lim(x→4)[(4-x)/(4-2√x)]

= lim(x→4)[(4-x)/2(2-√x)]

=lim(x→4)[(4-x)(2+√x)/2(2-√x)(2+√x)] Rationalize

=lim(x→4)[(4-x)(2+√x)/2(4-x)]

=lim(x→4)[((2+√x))/2]

=(2+√4)/2=(2+2)/2=4/2=2


I hope you understand