How do you rationalize the denominator and simplify $\frac{3}{t - \sqrt{2}}$ $3/(t-sqrt2)$ ?

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How do you rationalize the denominator and simplify $\frac{3}{t - \sqrt{2}}$ $3/(t-sqrt2)$ ?

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Answer 1 · 2017-08-24T23:03:33

See a solution process below:

Explanation:

To rationalize the denominator, or, in other words, remove the radicals from the denominator, we need to multiply this fraction by the appropriate form of $1$ $1$ .

We can use this quadratic rule to simplify this expression:

$(x + y) (x - y) = x^{2} - y^{2}$ $(color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - color(blue)(y)^2$

$\frac{t + \sqrt{2}}{t + \sqrt{2}} \times \frac{3}{t - \sqrt{2}} \Rightarrow \frac{3 (t + \sqrt{2})}{t^{2} - {(\sqrt{2})}^{2}} \Rightarrow$ $(color(red)(t) + color(blue)(sqrt(2)))/(color(red)(t) + color(blue)(sqrt(2))) xx 3/(color(red)(t) - color(blue)(sqrt(2))) => (3(color(red)(t) + color(blue)(sqrt(2))))/(color(red)(t)^2 - (color(blue)(sqrt(2)))^2) =>$

$\frac{3 t + 3 \sqrt{2}}{t^{2} - 2}$ $(3t + 3sqrt(2))/(t^2 - 2)$

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How do you rationalize the denominator and simplify $\frac{3}{t - \sqrt{2}}$ $3/(t-sqrt2)$ ?

1 Answer

Explanation:

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