# Calculating $\lim_{x \rightarrow 1}(\frac{x^2-\sqrt x}{\sqrt x-1})$ algebraically

I'm trying to calculate $\lim_\limits{x \rightarrow 1}(\frac{x^2-\sqrt x}{\sqrt x-1})$ algebraically and I've pretty much tried everything I can think of and I keep getting the limit to be $\frac{0}{0}$ which is obviously not right. I've tried multiplying the numerator and denominator by the conjugate of the denominator, I've tried using the difference of two squares on the numerator and I've tried dividing the rational function by $x^2$ but I keep on getting the wrong answer.

• factor out $1-\sqrt{x}$ in the numerator and cancel out with the denominator. – baby bunny Oct 19 '17 at 20:22

let $\sqrt { x } =t$ then
$$\lim _{ x\rightarrow 1 }{ \frac { x^{ 2 }-\sqrt { x } }{ \sqrt { x } -1 } } =\lim _{ t\rightarrow 1 }{ \frac { t^{ 4 }-t }{ t-1 } } =\lim _{ t\rightarrow 1 }{ \frac { t\left( t-1 \right) \left( { t }^{ 2 }+t+1 \right) }{ t-1 } } =3\\$$