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

1 Answer
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)