Simplify #(sqrt(1+2x)-3)/(sqrt(x)-2)# ?

1 Answer
sankarankalyanam
Aug 2, 2018

#=> (sqrt(x (1 + 2x))+ 2 sqrt(1 + 2x) - 3 sqrt x - 6) / (x - 4)#

Explanation:

#(sqrt(1 + 2x) - 3) / (sqrtx - 2)#

Multiply the nr. and dr. by the conjugate of the dr. to rationalise the dr.

#=>( (sqrt(1 + 2x) - 3) * (sqrtx + 2)) / ((sqrtx - 2) * (sqrtx + 2))#

#=> (sqrt(x (1 + 2x))+ 2 sqrt(1 + 2x) - 3 sqrt x - 6) / (x - 4)#

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