Simplify $\frac{\sqrt{1 + 2 x} - 3}{\sqrt{x} - 2}$ $(sqrt(1+2x)-3)/(sqrt(x)-2)$ ?

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Simplify $\frac{\sqrt{1 + 2 x} - 3}{\sqrt{x} - 2}$ $(sqrt(1+2x)-3)/(sqrt(x)-2)$ ?

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Answer 1 · 2018-08-02T02:18:17

$\Rightarrow \frac{\sqrt{x (1 + 2 x)} + 2 \sqrt{1 + 2 x} - 3 \sqrt{x} - 6}{x - 4}$ $=> (sqrt(x (1 + 2x))+ 2 sqrt(1 + 2x) - 3 sqrt x - 6) / (x - 4)$

Explanation:

$\frac{\sqrt{1 + 2 x} - 3}{\sqrt{x} - 2}$ $(sqrt(1 + 2x) - 3) / (sqrtx - 2)$

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

$\Rightarrow \frac{(\sqrt{1 + 2 x} - 3) \cdot (\sqrt{x} + 2)}{(\sqrt{x} - 2) \cdot (\sqrt{x} + 2)}$ $=>( (sqrt(1 + 2x) - 3) * (sqrtx + 2)) / ((sqrtx - 2) * (sqrtx + 2))$

$\Rightarrow \frac{\sqrt{x (1 + 2 x)} + 2 \sqrt{1 + 2 x} - 3 \sqrt{x} - 6}{x - 4}$ $=> (sqrt(x (1 + 2x))+ 2 sqrt(1 + 2x) - 3 sqrt x - 6) / (x - 4)$

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Simplify $\frac{\sqrt{1 + 2 x} - 3}{\sqrt{x} - 2}$ $(sqrt(1+2x)-3)/(sqrt(x)-2)$ ?

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Simplify $\frac{\sqrt{1 + 2 x} - 3}{\sqrt{x} - 2}$ $(sqrt(1+2x)-3)/(sqrt(x)-2)$ ?